A Magnetically Capsule Robot for Biomedical Application by Qiang Fu, Xi Zhang, Songyuan Zhang, Chunliu Fan, Zhuocong Cai, Lili Wang

“…This paper is based on the kinetic energy theorem, combined with the principle of spiral mechanism in mechanical design foundation to construct a calculation method of energy utilization and to improve the control effect of capsule robot, suitable for the human gastrointestinal tract precise control of capsule robot to perform a variety of complex tasks. …”
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On-shell approach to black hole mergers by Katsuki Aoki, Andrea Cristofoli, Yu-tin Huang

“…Up to sub-subleading order in spin, this matches the classical soft graviton theorem. We conclude with a comparison to black hole perturbation theory, which gives complementary amplitudes which are non-perturbative in the gravitational coupling but to leading order in the extreme mass ratio limit. …”
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Nonlinear Langevin dynamics via holography by Bidisha Chakrabarty, Joydeep Chakravarty, Soumyadeep Chaudhuri, Chandan Jana, R. Loganayagam, Akhil Sivakumar

“…The local effective theory obeys the recently proposed non-linear fluctuation dissipation theorem relating the non-Gaussianity of thermal noise to the thermal jitter in the damping constant. …”
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Mathematical modelling and forecasting of the Lithuanian export by Virmantas Kvedaras, Rimantas Rudzkis

“…Although according to the Granger representation theorem each finite order VAR has a respective ECM, it is known that, in general, co-integrated (in level) process does not admit a pure VAR representation in first differences. …”
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Macroscopic Expressions of Molecular Adiabatic Compressibility of Methyl and Ethyl Caprate under High Pressure and High Temperature by Fuxi Shi, Qin Zhang, Jun Chen, Hamid Reza Karimi

“…The third was derived with introducing the pressure and temperature correction factors based on analogy to Lennard-Jones potential function and energy equipartition theorem. In wide range of temperatures (293<T/K<393) and pressures (0.1<P/MPa<210), which represent the typical values used in dynamic injection process for diesel engines, the calculated results consistency of three formulas demonstrated their effectiveness with the maximum 0.5384% OARD; meanwhile, the dependency on pressure and temperature of molecular compressibility was certified.…”
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Numerical characterization of the performance of counter-flow double-pipe heat exchanger using nanofluids for laminar flow regime by Abdulaziz S. Alhulaifi

“…In comparison to other nanofluids, lower density nanofluids, such Ash/H2O, had larger pressure drop and pumping power. The Buckingham Pi theorem was used to perform nondimensionalization analysis. …”
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A Ship Collision Analysis Program Based on Upper Bound Solutions and Coupled with a Large Rotational Ship Movement Analysis Tool by Hervé Le Sourne, Nicolas Besnard, Cedric Cheylan, Natacha Buannic

“…To do this, the so-called upper bound theorem is applied to calculate internal forces and energies of any substructure involved in the ships crushing process. …”
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Design and Analysis of Power-function-sine Flexure Hinges by Li Jiabiao, Zhao Yang, Wu Qingwen, Mu Deqiang, Liu Changru, Hu Jinxin

“…The calculation formula of compliance and rotation accuracy of the flexure hinge is derived by using Castigliano's second theorem. The finite element simulation analysis and theoretical value calculation of compliance and rotation accuracy are carried out by taking different parameter values. …”
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Methane detection approach based on THz wave absorber by Alireza Barati Haghverdi, Ilghar Rezaei, Amir Ali Mohammad Khani, Toktam Aghaee

“…The equivalent impedance can reveal the absorption response of the structure with the aim of impedance matching or maximum power transmission theorem. Interestingly, the impedance modeling converges to the numerical full-wave simulation, verifying efficient mathematical modeling. …”
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Superfluid transition in quasi-two-dimensional disordered dipolar Fermi gases by Pinchenkova, Victoria Y., Matveenko, Sergey I., Yudson, Vladimir I., Shlyapnikov, Georgy V.

“…The dipole-dipole interaction amplitude is momentum dependent, which violates the Anderson theorem claiming that the weak disorder has practically no influence on the superfluid transition temperature in the weakly interacting regime. …”
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Holes Detection in Anisotropic Sensornets: Topological Methods by Wei Wei, Xiao-Lin Yang, Pei-Yi Shen, Bin Zhou

“…To address this issue, we propose a solution, named PPA based on Poincare-Perelman Theorem, to judge whether there are holes in WSNs-monitored areas. …”
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A Discrete Dipole Approximation Solver Based on the COCG-FFT Algorithm and Its Application to Microwave Breast Imaging by Samar Hosseinzadegan, Andreas Fhager, Mikael Persson, Paul Meaney

“…The computation costs for multiplying the block matrices times a vector can be dramatically accelerated by expanding each Toeplitz matrix to a circulant matrix for which the convolution theorem is applied for fast computation utilizing the fast Fourier transform (FFT). …”
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The Existence of Positive Solutions for a Fourth-Order Difference Equation with Sum Form Boundary Conditions by Yanping Guo, Xuefei Lv, Yude Ji, Yongchun Liang

“…We consider the fourth-order difference equation: Δ(z(k+1)Δ3u(k-1))=w(k)f(k,u(k)),  k∈{1,2,…,n-1} subject to the boundary conditions: u(0)=u(n+2)=∑i=1n+1g(i)u(i), aΔ2u(0)-bz(2)Δ3u(0)=∑i=3n+1h(i)Δ2u(i-2), aΔ2u(n)-bz(n+1)Δ3u(n-1)=∑i=3n+1h(i)Δ2u(i-2), where a,b>0 and Δu(k)=u(k+1)-u(k) for k∈{0,1,…,n-1},  f:{0,1,…,n}×[0,+∞)→[0,+∞) is continuous. h(i) is nonnegative i∈{2,3,…,n+2}; g(i) is nonnegative for i∈{0,1,…,n}. Using fixed point theorem of cone expansion and compression of norm type and Hölder’s inequality, various existence, multiplicity, and nonexistence results of positive solutions for above problem are derived, which extends and improves some known recent results.…”
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Constructing Multiple-Objective Portfolio Selection for Green Innovation and Dominating Green Innovation Indexes by Meng Li, Kezhi Liao, Yue Qi, Tongyang Liu

“…As the originality, we prove in a theorem that there typically exists a curve on the efficient surface so all portfolios on the curve dominate the green innovation index. …”
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Position/Force Tracking Impedance Control for Robotic Systems with Uncertainties Based on Adaptive Jacobian and Neural Network by Jinzhu Peng, Zeqi Yang, Tianlei Ma

“…Based on the Lyapunov stability theorem, it is proved that all the signals in closed-loop system are bounded and the position and velocity errors are asymptotic convergence to zero. …”
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Generalized Moisil-Théodoresco Systems and Cauchy Integral Decompositions by Ricardo Abreu Blaya, Juan Bory Reyes, Richard Delanghe, Frank Sommen

“…Then, an ℝ0,m+1(r,p,q)-valued smooth function W defined in an open subset Ω⊂ℝm+1 is said to satisfy the generalized Moisil-Théodoresco system of type (r,p,q) if ∂xW=0 in Ω, where ∂x is the Dirac operator in ℝm+1. A structure theorem is proved for such functions, based on the construction of conjugate harmonic pairs. …”
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Stability Analysis of a Nonlinear Coupled Vibration Model in a Tandem Cold Rolling Mill by Xing Lu, Jie Sun, Guangtao Li, Zhenhua Wang, Dianhua Zhang

“…By using Hopf bifurcation theorem and Routh–Hurwitz determinant, the existence of the Hopf bifurcation point of the mill vibration system and bifurcation characteristics are analyzed. …”
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Multiple Positive Solutions of Singular Nonlinear Sturm-Liouville Problems with Carathéodory Perturbed Term by Yuefeng Han, Xinguang Zhang, Lishan Liu, Yonghong Wu

“…By employing a well-known fixed point theorem, we establish the existence of multiple positive solutions for the following fourth-order singular differential equation Lu=p(t)f(t,u(t),u′′(t))-g(t,u(t),u′′(t)),0<t<1,α1u(0)-β1u'(0)=0,γ1u(1)+δ1u'(1)=0,α2u′′(0)-β2u′′′(0)=0,γ2u′′(1)+δ2u′′′(1)=0, with αi,βi,γi,δi≥0 and βiγi+αiγi+αiδi>0,    i=1,2, where L denotes the linear operator Lu:=(ru′′′)'-qu′′,r∈C1([0,1],(0,+∞)), and q∈C([0,1],[0,+∞)). …”
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Mechanical Model for Shear Friction Capacity of Concrete at Construction Joints by Seung-Jun Kwon, Keun-Hyeok Yang, Ju-Hyun Mun

“…The integrated mechanical model for the monolithic interface, derived from the upper-bound theorem of concrete plasticity, was also modified to estimate the shear friction strength of the construction joints. …”
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Prediction of the Collapse Region Induced by a Concealed Karst Cave above a Deep Highway Tunnel by Fu Huang, Di Wang, Yuan Feng, Min Zhang

“…A prediction method of the collapse region induced by a concealed karst cave above a deep highway tunnel is proposed on the basis of the upper bound theorem of limit analysis. An analytical expression of the collapse surface is derived from the variational principle. …”
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