Closed-form heave solutions for expansive soils Por Rao, R. Rama, Rahardjo, Harianto, Fredlund, Delwyn G.

“...In all cases, the soil deposit is assumed to be homogeneous, and the swelling pressure is assumed to be constant with depth. The closed-form solutions are presented for the calculation of total heave when: (1) A portion or the entire “active depth” is wetted; (2) a portion of the expansive soil is excavated; and (3) the excavated portion is backfilled with a nonexpansive soil....”
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Closure to “closed-form heave solutions for expansive soils” Por Rao, R. Rama, Rahardjo, Harianto, Fredlund, Delwyn G.

“...The laboratory procedures for testing expansive soils have also been essentially standardized. ...”
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Nonstationary shot noise modeling of neuron membrane potentials by closed-form moments and Gram-Charlier expansions Por Privault, Nicolas

“...As an application, we derive closed-form Gram-Charlier density expansions that show how the probability density functions of potentials in such models differ from their Gaussian diffusion approximations. ...”
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Closed-form modeling of neuronal spike train statistics using multivariate Hawkes cumulants Por Privault, Nicolas, Thieullen, Michèle

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Closed-Form Method for Unified Far-Field and Near-Field Localization Based on TDOA and FDOA Measurements Por Weishuang Gong, Xuan Song, Chunyu Zhu, Qi Wang, Yachao Li

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Kink soliton solution of integrable Kairat-X equation via two integration algorithms Por Raed Qahiti, Naher Mohammed A. Alsafri, Hamad Zogan, Abdullah A. Faqihi

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Novel solitary wave solutions and bifurcation analysis of multispecies dusty plasma consisting of cold dust grains Por Reem Altuijri, Nauman Raza, Muhammad Umair, Muhammad Farman, Hanadi M. AbdelSalam, Abaker A. Hassaballa, Hegagi M. Ali

“...This study focuses on revealing closed-form solutions for traveling waves in the nonlinear dynamical model of dust-acoustic waves in multispecies of dusty plasma. ...”
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Modulation Instability and Dynamical Analysis of New Abundant Closed-Form Solutions of the Modified Korteweg–de Vries–Zakharov–Kuznetsov Model With Truncated M-Fractional Derivativ... Por Md. Shafiqul Islam, Md. Mamunur Roshid, Mahtab Uddin, Ashek Ahmed

“...Under the conditions of the numerical values of the free parameters, the obtained closed-form solutions provided some novel phenomena such as antikink shape wave, dark bell shape, collision of kink and periodic lump wave, periodic wave, collision of antikink and periodic lump wave, collision of linked lump wave with kink shape, periodic lump wave by using improved F-expansion method and kink shape, diverse type of periodic wave, singular soliton, and bright bell and dark bell-shape wave phenomena by using unified solver method. ...”
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Design of multi-bandgap metamaterial plate based on composite cylindrical resonators Por Zhi Miao, Jianfei Yin, Yu Yang, Yibo Ke, Zhoufu Zheng, Xiaoming Geng, Qian Wang

“...Theoretical models employing the plane wave expansion method are developed to compute the band structures of the CLRMP. ...”
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Matched Asymptotic Expansions for Valuing Spread Options Por Charara, R

“...The problem with spread options is that there are no closed- form formulae to price or hedge them. In this paper, we use matched asymptotic expansions in order to price spread options. ...”

Asymptotic expansions and distribution properties for diffusion processes Por She, Qihao

“...For application, we derive a closed-form analytical approximations formula in terms of series expansion for the option prices, implied volatility and delta under the 2-Hypergeometric stochastic volatility model with correlated Brownian motions. ...”
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FINITE CAVITY EXPANSION IN DILATANT SOILS - LOADING ANALYSIS Por Yu, H, Houlsby, G

“...Closed form solutions for the stress and displacement fields in the soil during the expansion of the cavity are given. ...”

M2-M5 giant graviton expansions Por Hirotaka Hayashi, Tomoki Nosaka, Tadashi Okazaki

“...Abstract We examine the giant graviton expansions of the Coulomb and Higgs indices for the M2-brane SCFTs to find the closed-form expressions for the indices that encode the spectra of the 1/4-BPS M5-brane giant gravitons and the 1/3-BPS orbifold M5-brane giant gravitons. ...”
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Schur line defect correlators and giant graviton expansion Por M. Beccaria

“...Abstract We consider Schur line defect correlators in four dimensional N $$ \mathcal{N} $$ = 4 U(N) SYM and their giant graviton expansion encoding finite N corrections to the large N limit. ...”
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Giant graviton expansion of Schur index and quasimodular forms Por M. Beccaria, A. Cabo-Bizet

“...We exploit recent exact results about the Schur index of N $$ \mathcal{N} $$ = 4 U(N) SYM to evaluate the closed form of the brane indices appearing in the giant graviton expansion. ...”
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Spectral flow and the conformal block expansion for strings in AdS3 Por Sergio Iguri, Nicolas Kovensky, Julián H. Toro

“...Although the latter are not known in closed form, their conformal block expansion has been formally established. ...”
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New Application of the (G′/G)-Expansion Method for Thin Film Equations Por Wafaa M. Taha, M. S. M. Noorani, I. Hashim

“...The closed-form solution obtained via this method is in good agreement with the previously obtained solutions of other researchers. ...”
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Capacity of fully correlated MIMO system using character expansion of groups Por Ejaz Khan, Conor Heneghan

“...We use replica method and character expansions to calculate the capacity of correlated MIMO channel in closed form. ...”
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Vibration Analysis of Conical Shells by the Improved Fourier Expansion-Based Differential Quadrature Method Por Wanyou Li, Gang Wang, Jingtao Du

“...The original function is expressed as the Fourier cosine series combined with close-form auxiliary functions. Those auxiliary functions are introduced to ensure and accelerate the convergence of series expansion. ...”
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Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized G′/G-Expansion Method Por Sanjaya K. Mohanty, Apul N. Dev, Soubhagya Kumar Sahoo, Homan Emadifar, Geeta Arora

“...In this investigation, the exact solutions of variable coefficients of generalized Zakharov-Kuznetsov (ZK) equation and the Gardner equation are studied with the help of an extended generalized G′/G expansion method. The main objective of this study is to establish the closed-form solutions and dynamics of analytical solutions to the generalized ZK equation and the Gardner equation. ...”
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