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The time-dependent resilience of an in-service aging structure provides quantitative measure of the structural ability to prepare for, adapt to, withstand and recover from disruptive events. Resilience models have been proposed in the literature to evaluate the resilience of aging structures subjected to discrete load processes, which are, however, not applicable to handle resilience problems considering continuous load processes. In this paper, a new method is developed to evaluate the time-dependent resilience of aging structures subjected to a continuous load process. The proposed method serves as the complement of the existing resilience models addressing discrete load processes, and takes into account the aging effects of the structural resistance/capacity and the nonstationarity in loads as a result of climate change. A structure suffers from a damage state upon the occurrence of an upcrossing of the load effect with respect to the resistance/capacity, leading to the reduction of the performance function, followed by a recovery process that restores the performance. The proposed method enables the time-dependent resilience to be evaluated via a closed form solution. It is also revealed that, the proposed resilience model takes an extended form of the existing formula for upcrossing-based time-dependent reliability, thus establishing a unified framework for the two quantities. The applicability of the proposed method is demonstrated through examining the time-dependent resilience of a residential building subjected to wind load. The effects of key factors on resilience, including the nonstationarity and correlation structure of the load process, as well as the resistance/capacity deterioration scenario, are investigated through an example. In particular, the structural resilience would be overestimated if ignoring the potential impacts of climate change, which is a relatively non-conservative evaluation.

In this paper we derive the best constant for the following L^{\infty }-type Gagliardo-Nirenberg interpolation inequality \begin{equation*} \|u\|_{L^{\infty }}\leq C_{q,\infty,p} \|u\|^{1-\theta }_{L^{q+1}}\|\nabla u\|^{\theta }_{L^p},\quad \theta =\frac {pd}{dp+(p-d)(q+1)}, \end{equation*} where parameters q and p satisfy the conditions p>d\geq 1, q\geq 0. The best constant C_{q,\infty,p} is given by \begin{equation*} C_{q,\infty,p}=\theta ^{-\frac {\theta }{p}}(1-\theta)^{\frac {\theta }{p}}M_c^{-\frac {\theta }{d}},\quad M_c≔\int _{\mathbb {R}^d}u_{c,\infty }^{q+1} dx, \end{equation*} where u_{c,\infty } is the unique radial non-increasing solution to a generalized Lane-Emden equation. The case of equality holds when u=Au_{c,\infty }(\lambda (x-x_0)) for any real numbers A, \lambda >0 and x_{0}\in \mathbb {R}^d. In fact, the generalized Lane-Emden equation in \mathbb {R}^d contains a delta function as a source and it is a Thomas-Fermi type equation. For q=0 or d=1, u_{c,\infty } have closed form solutions expressed in terms of the incomplete Beta functions. Moreover, we show that u_{c,m}\to u_{c,\infty } and C_{q,m,p}\to C_{q,\infty,p} as m\to +\infty for d=1, where u_{c,m} and C_{q,m,p} are the function achieving equality and the best constant of L^m-type Gagliardo-Nirenberg interpolation inequality, respectively. [ABSTRACT FROM AUTHOR]

Considering that the exact solution for thermal buckling and post-buckling of the graphene platelets (GPLs)-reinforced composite beam in exposure to temperature changes has not been so far addressed, this problem is investigated in this research. The governing equations of the beam under thermal buckling load were acquired using the principle of virtual work, first-order shear deformation theory, and von Kármán strain field. The effective properties of the materials were then determined using the Halpin–Tsai model and rule of mixtures. Three coupled nonlinear equations are established and solved directly. Results are obtained for beams with clamped and simply supported edges. After validating the results, the effects of changing the GPLs distribution pattern and weight fraction changes on the critical thermal buckling load were evaluated. It is highlighted that for beams with simply supported edges and asymmetric distribution of material properties, the response is not of the bifurcation type. [ABSTRACT FROM AUTHOR]

This paper considers the fluid flow through a porous medium containing intersecting fractures and presents three main analytical findings, namely: (1) mass exchange between fractures and surrounding matrix at the fracture intersection; (2) fluid potential solution (pressure field) within the whole domain under the form of a single singular integral equation; and (3) closed‐form solutions of fluid flow in and around a crack disc under a far field pressure gradient. The crack is represented mathematically by a 2D smooth surface (i.e., zero thickness) within a 3D porous medium, while physically by a constant aperture. The fluid flow within the crack obeys Poisseuille's law, while Darcy's law is used to represent the fluid flow in the surrounding matrix. The general solution of pressure field for the general case of multiple intersecting cracks is firstly derived under a singular integral equation form. The mass exchange between the porous matrix and the crack, as well as the mass conservation at the intersection between cracks are the keys to obtaining this general solution. Then, the general solution is written for the case of a single crack. Rigorous derivation of the latter equation allows obtaining a closed‐form solution of flow through a single crack. Introducing this solution of flow into the general equation gives the pressure field around the crack. The solution derived in this paper for a crack disk with Poisseuille's flow is slightly different from the well‐known Eshelby's solution for the case of flattened inclusion in which the flow obeys Darcy's law. [ABSTRACT FROM AUTHOR]

In the current effort, the effects of entropy generation and electro-osmotic driven peristaltic flow of non-Newtonian Williamson liquid in a curved micro-channel is investigated. Formulation of the problem is conducted in a wave frame of reference. Due to the complexity of non-Newtonian fluid, the analytical solutions of non-linear coupled equations are not easy to obtain and are very rarely found in the literature. For analytical solutions, the governing equations are reduced in the form of the Bessel function. The electric double layer is employed as a result of a zeta potential of about 25 mV. The low Reynolds number and long wavelength approximations are taken into account. Graphical analysis has been carried out for velocity, temperature and entropy for physical parameters. It is noted that the Brinkmann number enhances the temperature. The results of this model will be extremely helpful in designing electro-peristaltic pumps for thermal systems. [ABSTRACT FROM AUTHOR]

Copyright of International Economics / Economia Internazionale is the property of Camera di Commercio di Genova and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

As an aircraft or spacecraft ascends, the atmospheric pressure drops. If the internal pressure is not released, a pressure differential develops on the facesheet. With an in-plane load from vehicle acceleration as well, the pressure and in-plane load may cause failure. Vented sandwich structures are strongly preferred since they release the internal pressure; however, special cases still require an unvented design. This paper provides an analysis and test methodology for unvented sandwich structures. Parametric studies of facesheet-core debonding and buckling were conducted via finite element analysis, considering geometric, material, and load parameters. Design curves based on the key nondimensional parameters were tuned to the data from the parametric study, providing a tool to predict facesheet-core debond failure. Examples of how to use the design curves in practical applications are provided. [ABSTRACT FROM AUTHOR]

It is suggested by many works on solar stills that water thickness should be kept as low as possible to reduce its thermal inertia and obtain best results. However, when external heat addition is employed by an internal exchanger, the amount of heat addition is also affected by the still water thickness, and so, the above-mentioned finding could be proved incorrect. In this context, here, the performance of a solitary basin solar still aided by external heat addition has been revisited. At first, an expression for the maximum possible effectiveness of the above-mentioned exchanger is derived. Based on this, improved closed form solutions for the still water temperature and still productivity have been obtained using integrating factor method. It is shown that the closed form solutions presented here are mathematically superior to other analytical solutions available in the literature on the topic, in the sense that the present ones are strictly analytical, while all others use an iterative algorithm to solve the pertinent differential equation. Contrary to the available studies on solar stills which suggest keeping the water thickness to its minimum possible value, the present results reveal an optimum thickness of the same to maximize the system productivity. Using the optimized still water thickness, about 35 and 41% enhancement in the daily and annual productivity respectively can be acquired with respect to the thickness suggested by the available literature. The optimum value stems from a trade-off between the efficiency of external heat addition and the thermal inertia of the water mass. This work therefore suggests the thickness of water mass in heat exchanger–based solar stills to be designed at an optimum value for best results, and also provides useful improved expressions for performance assessment of such stills. [ABSTRACT FROM AUTHOR]

As is well known, multi-factor stochastic volatility models are necessary to capture the market accurately in pricing financial derivatives. However, the multi-factor models usually require too many parameters to be calibrated efficiently and they do not lead to an analytic pricing formula. The double Heston model is one of them. The approach of this paper for this difficulty is to rescale the double Heston model to reduce the number of the model parameters and obtain a closed form analytic solution formula for variance swaps explicitly. We show that the rescaled double Heston model is as effective as the original double Heston model in terms of fitting to the VIX market data in a stable condition and yet the computing time is much less than that under the double Heston model. However, in a turbulent situation after the start of the COVID-19 pandemic in 2020, we acknowledge that even the double Heston model fails to capture the market accurately. [ABSTRACT FROM AUTHOR]

Abstract This study investigates the influence of a circular crack breaker on mode-III deformation behavior of a semi-infinite crack in a homogeneous, elastic orthotropic material subjected to longitudinal shear loads. The Galilean transformation is employed to convert the governing wave equation to Laplace’s equation which is time independent, rendering the problem amenable to analysis within the realm of the classical theory of two-dimensional elasticity. Considering the geometrical configuration of the problem, the analytical solution of the problem is possible if the problem is transformed using the appropriate mapping function. Our construction of a holomorphic function that maps the circular hole into a straight line with the edge terminating at the origin is a novelty which enables the use of integral transform method to obtain an analytic solution of the displacement, leading to closed-form expression for mode-III stress intensity factor, $$K_{111}$$ K 111 . The asymptotic values of the fields are obtained and shown to depend on the radius of the crack breaker. A parametric study shows that, for a fixed loading interval, a crack breaker of larger radius leads to increased stress intensity factor.

A theoretical analysis of electro-osmosis peristaltic flow of generalized Newtonian fluid bounded in a complex wavy divergent channel is performed. There are many complex rheological generalized Newtonian fluids, out of which Ellis fluid model is considered to approximate the fluid present within the channel. The flow equations are modelled using balances of mass and momentum while the body force term is introduced using well known Poisson equation. An analytical solution to the governing flow equations is presented and the closed form expressions for longitudinal velocity, flow rate and stream function are developed. The numerical solution of pressure rise is obtained via NIntegrate build in command of Mathematica 12.3. Influence of diverse rheological and electrical parameters on flow characteristics are analysed via plots.

A mechanical system, in general, undergoes vibrational motion when the system is subjected to a tension or an external force. One of the examples of such a system is a cantilever beam when it is exposed to a bending action. When the tension is released, the cantilever beam suffers from the oscillations until the strain energy is totally released through the damping characteristics of the cantilever beam. Depending on the stiffness and damping factors of the beam, the vibrational motion can be non-linear; in which case, the analytical solution becomes challenging formulating the flexural characteristics of the beam. Although numerical solution for the non-linear problem is possible, the analytical solution provides useful information between the mechanical response and the cantilever beam characteristics. In the present study, the analytical solution of the non-linear equations governing the motion of the cantilever beam is presented. The governing equation is linearized incorporating the Lie-Tresse linearization method. The closed form solution for the displacement of the cantilever beam is reduced to a linear solution after introducing the appropriate beam characteristics. The dynamic behavior of the flexural motion due to non-linear and linear cantilever beams are compared.

In this paper, a particular inhomogeneous inclusion problem is studied. In the problem, Eshelby's eigenstrain takes the type x m y n , where m + n = 2, and the remote loadings σ x ∞ , σ y ∞ are applied. In the solution, the complex variable method is used. The continuity conditions along the interface of the matrix and the inclusion are formulated exactly. Because the stress field is no longer uniform in inclusion in this case, the studied problem has an inherent difficulty. After some manipulation, the final result for stress components σ x in , σ y in and σ xy in in inclusion are obtainable. In the present study, σ x in , σ y in and σ xy in are no longer uniform. [ABSTRACT FROM AUTHOR]

Copyright of Chinese Journal of Computational Mechanics / Jisuan Lixue Xuebao is the property of Chinese Journal of Computational Mechanics Editorial Office, Dalian University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, the dynamic stability analysis of a rolling airframe actuated by one pair ON-OFF actuator using linear theory is presented via developing a new closed form solution. The effect of discontinuous forcing term on rolling airframe stability is studied. In contrast to tricyclic motion with constant forcing term (constant non-homogeneous term) in which only the amplitude of nutation and precession is affected, it is found that ON-OFF control affects both amplitude and phase of nutation and precession motions. In the case of discontinuous control surface, there are two sources for resonance instability. Finally, through simulation results of closed form solutions, a comparison between airframe’ response to ideal and real ON-OFF command is achieved. The effect of ON-OFF control on angular motion is also evaluated.

Purpose – Fractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to their importance in the nature of real world. In this article, the autors suggest a productive technique, called the rational fractional (DξαG/G)-expansion method, to unravel the nonlinear space-time fractional potential Kadomtsev–Petviashvili (PKP) equation, the nonlinear space-time fractional Sharma–Tasso–Olver (STO) equation and the nonlinear space-time fractional Kolmogorov–Petrovskii–Piskunov (KPP) equation. A fractional complex transformation technique is used to convert the considered equations into the fractional order ordinary differential equation. Then the method is employed to make available their solutions. The constructed solutions in terms of trigonometric function, hyperbolic function and rational function are claimed to be fresh and further general in closed form. These solutions might play important roles to depict the complex physical phenomena arise in physics, mathematical physics and engineering. Design/methodology/approach – The rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is of the form U(ξ)=∑i=0nai(DξαG/G)i/∑i=0nbi(DξαG/G)i. Findings – Achieved fresh and further abundant closed form traveling wave solutions to analyze the inner mechanisms of complex phenomenon in nature world which will bear a significant role in the of research and will be recorded in the literature. Originality/value – The rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is newly established and productive.

In the current effort, the effects of entropy generation and electro-osmotic driven peristaltic flow of non-Newtonian Williamson liquid in a curved micro-channel is investigated. Formulation of the problem is conducted in a wave frame of reference. Due to the complexity of non-Newtonian fluid, the analytical solutions of non-linear coupled equations are not easy to obtain and are very rarely found in the literature. For analytical solutions, the governing equations are reduced in the form of the Bessel function. The electric double layer is employed as a result of a zeta potential of about 25 mV. The low Reynolds number and long wavelength approximations are taken into account. Graphical analysis has been carried out for velocity, temperature and entropy for physical parameters. It is noted that the Brinkmann number enhances the temperature. The results of this model will be extremely helpful in designing electro-peristaltic pumps for thermal systems.

This study investigates the influence of a circular crack breaker on mode-III deformation behavior of a semi-infinite crack in a homogeneous, elastic orthotropic material subjected to longitudinal shear loads. The Galilean transformation is employed to convert the governing wave equation to Laplace's equation which is time independent, rendering the problem amenable to analysis within the realm of the classical theory of two-dimensional elasticity. Considering the geometrical configuration of the problem, the analytical solution of the problem is possible if the problem is transformed using the appropriate mapping function. Our construction of a holomorphic function that maps the circular hole into a straight line with the edge terminating at the origin is a novelty which enables the use of integral transform method to obtain an analytic solution of the displacement, leading to closed-form expression for mode-III stress intensity factor, K 111 . The asymptotic values of the fields are obtained and shown to depend on the radius of the crack breaker. A parametric study shows that, for a fixed loading interval, a crack breaker of larger radius leads to increased stress intensity factor. [ABSTRACT FROM AUTHOR]

A theoretical analysis of electro-osmosis peristaltic flow of generalized Newtonian fluid bounded in a complex wavy divergent channel is performed. There are many complex rheological generalized Newtonian fluids, out of which Ellis fluid model is considered to approximate the fluid present within the channel. The flow equations are modelled using balances of mass and momentum while the body force term is introduced using well known Poisson equation. An analytical solution to the governing flow equations is presented and the closed form expressions for longitudinal velocity, flow rate and stream function are developed. The numerical solution of pressure rise is obtained via N I n t e g r a t e build in command of Mathematica 12.3. Influence of diverse rheological and electrical parameters on flow characteristics are analysed via plots. [ABSTRACT FROM AUTHOR]

In this paper, we present a detailed study of the following difference equation xn+1 = αn/1 + xnxn-1, n N0, where the sequence (an)n=0 is positive, real, periodic with period two and the initial values x-1, x0 are nonnegative real numbers. By this study, we determine global behavior of positive solutions of the above mentioned equation. We also give closed forms of its general solution. [ABSTRACT FROM AUTHOR]

Reliability is one of the important factors in production inventory system as well as in the demand of the products. During a production process, the products which are more perfect with higher reliability increase the demand of the product whereas credit facility is also one of the popular business strategies. Combining these two concepts in together, we have described and analyzed mathematically a production inventory model with a partial credit facility and the reliability effect on the production system in which the customers’ demand is dependent on the price of the products and deterioration rate is considered to be constant. In this proposed model, trade credit policy on both the manufacturer and customers is introduced by taking into account all the possible situations on the basis of allowed credit periods. Under these situations, taking all possible cases for the manufacturer credit period as well as customers’ credit period, seven non-linear optimization problems for the proposed model are obtained. Since the corresponding optimization problems associated to this model are highly non-linear, we have found closed form optimal solution of the corresponding each of these objective functions by using Taylor’s series approximation technique. The convexity of the objective function of each non-linear problem is also investigated graphically. Finally, to validate the proposed model a set of seven numerical examples have been simultaneously solved and a sensitivity analysis is executed to notice the behavior of the parameters on the optimal solution.

Existing masonry buildings and infrastructures are often characterized by curved elements like arches, where the settlements could induce damages up to compromising their stability. Curved elements are very sensitive to settlements due to the modification of the lateral thrust. The effects of settlements could be very critical on heritage buildings, where the intrados of curved elements are often characterized by decorated plasters. These issues caused by settlements are very important also in the infrastructures, where the displacement of the foundations could affect the main structural elements. When dealing with existing heritage buildings the analysis cannot be focused on the ultimate state only. In order to preserve the heritage value, it is important to refer to elastic behaviour to minimize the damages at serviceability limit state (e.g., newly defined artistic limit state). In this work, an existing theory has been used to obtain the closed-form solution for a specific curved system (i.e., Standard arch). The behaviour of semi-circular and parabolic curved elements is investigated under several load conditions of vertical loads and settlements. The solutions were numerically estimated according to the Principle of Virtual Works and are dimensionless in order to obtain generalizable results. A parametrical analysis was performed, providing several useful design charts to assess the impact of settlements and vertical loads on the behaviour of curved elements. The closed-form solution derived for standard arch if applied to different cases yields to approximated solutions and the scatter was estimated by comparing them with refined numerical evaluations. The outcomes of this work are useful tools to assess the sensitivity to structural damage of curved elements under settlements. [ABSTRACT FROM AUTHOR]

The instability of nanobeams rested on two-parameter elastic foundations is studied through the Bernoulli–Euler beam theory and the stress-driven nonlocal elasticity model. The size-dependency is incorporated into the formulation by defining the strain at each point as an integral convolution in terms of the stresses in all the points and a kernel. The nonlocal elasticity problem in a bounded domain is well-posed and inconsistencies within the Eringen nonlocal theory are overcome. Excellent agreement is found with the results in the literature, and new insightful results are presented for the buckling loads of nanobeams rested on the Winkler and Pasternak foundations. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Signal Processing is the property of Journal of Signal Processing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

High-rise structures are characterized as wind-sensitive vertical structures, estimating the wind-induced vibration response is a key to the structural design procedure. This study presented universal wind load spectral models for high-rise structures, including tri-para and κ model for along-wind load characterized by power dissipating with frequency and analog filter model for cross-wind load dominant by power concentration induced by vortex excitation. The spectral models appear to provide good agreement with wind tunnel data of buildings with various configurations. With analog filter approach, the along-wind spectra can be approximated by a linear filter polynomial and the cross-wind spectra is expressed by a quadratic filter polynomial. Thus forming a simple differential equation for the along- and cross-wind excitation based on a pseudo idea white noise. The closed form solutions to the wind-induced responses are derived based on analog filter approach. The Lyapunov equations are also provided in the state-space for high-rise structures with and without extra damping devices. The presented closed form solutions can provide a powerful tool in codification and vibration control optimization.

In this paper, the thermal stress analysis for a cusp-type crack problem under remote thermal loading is carried out. The remote thermal loading is applied at infinite place. Along the cusp-type crack, two kinds of thermal condition are assumed: (a) the thermal insulated condition, and (b) vanishing temperature condition. The thermal temperature and the stress fields are evaluated by using the complex mapping technique and the complex potentials. It is found that the obtained stress intensity factors (SIF) are quite different for the two mentioned boundary conditions.

Under the remote thermal loading, the thermal stress analysis for a hypocycloid-type crack is carried out. Two kinds of thermal conditions are assumed along the hypocycloid-type crack. Among them, one is the thermal insulated condition and the other is the vanishing temperature condition along the crack face. By using the complex variable function method in conjunction with the conformal mapping technique, a closed form solution for stress intensity factors (SIFs) is obtained. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic stability analysis of a rolling airframe actuated by one pair ON-OFF actuator using linear theory is presented via developing a new closed form solution. The effect of discontinuous forcing term on rolling airframe stability is studied. In contrast to tricyclic motion with constant forcing term (constant non-homogeneous term) in which only the amplitude of nutation and precession is affected, it is found that ON-OFF control affects both amplitude and phase of nutation and precession motions. In the case of discontinuous control surface, there are two sources for resonance instability. Finally, through simulation results of closed form solutions, a comparison between airframe' response to ideal and real ON-OFF command is achieved. The effect of ON-OFF control on angular motion is also evaluated. [ABSTRACT FROM AUTHOR]

In this paper we like to explore the full power of Adomian decomposition method (ADM), specially its symbolic capability. We will demonstrate the standard ADM and ADM with integration factor to compute explicit closed form solutions of first order scalar partial differential equations with unprescribed initial conditions, and even with parameters. These features are those numerical methods fail to do. Our examples include linear/nonlinear, constant/variable coefficients and homogeneous/nonhomogeneous equations. The method of characteristics is also tested and compared with these two ADM methods. We conclude that ADM is excellent among all existing methods. [ABSTRACT FROM AUTHOR]

The paper proposes an expanded version of the Local Variance Gamma model of Carr and Nadtochiy by adding drift to the governing underlying process. Still in this new model it is possible to derive an ordinary differential equation for the option price which plays a role of Dupire's equation for the standard local volatility model. It is shown how calibration of multiple smiles (the whole local volatility surface) can be done in such a case. Further, assuming the local variance to be a piecewise linear function of strike and piecewise constant function of time this ODE is solved in closed form in terms of Confluent hypergeometric functions. Calibration of the model to market smiles does not require solving any optimization problem and, in contrast, can be done term-by-term by solving a system of non-linear algebraic equations for each maturity. This is much faster as compared with calibration which requires solving the Dupire PDE. [ABSTRACT FROM AUTHOR]

Reliability is one of the important factors in production inventory system as well as in the demand of the products. During a production process, the products which are more perfect with higher reliability increase the demand of the product whereas credit facility is also one of the popular business strategies. Combining these two concepts in together, we have described and analyzed mathematically a production inventory model with a partial credit facility and the reliability effect on the production system in which the customers' demand is dependent on the price of the products and deterioration rate is considered to be constant. In this proposed model, trade credit policy on both the manufacturer and customers is introduced by taking into account all the possible situations on the basis of allowed credit periods. Under these situations, taking all possible cases for the manufacturer credit period as well as customers' credit period, seven non-linear optimization problems for the proposed model are obtained. Since the corresponding optimization problems associated to this model are highly non-linear, we have found closed form optimal solution of the corresponding each of these objective functions by using Taylor's series approximation technique. The convexity of the objective function of each non-linear problem is also investigated graphically. Finally, to validate the proposed model a set of seven numerical examples have been simultaneously solved and a sensitivity analysis is executed to notice the behavior of the parameters on the optimal solution. [ABSTRACT FROM AUTHOR]

Various methods have been proposed for passive localization by using a network of sensors measuring different parameters such as the angle of arrival (AOA), time difference of arrival (TDOA), Doppler frequency difference of arrival (FDOA), differential received signal strength (DRSS), the gain ratio of arrival (GROA), or a combination of these pieces of information. In this paper, a method for target localization based on power of received signal in multiple stations has been proposed for two scenarios. In one scenario, the receiving antennas are omnidirectional and in the other scenario they are directional. We have derived a closed-form solution for source localization in the first scenario and we have proposed two methods (i.e., random search and Taylor series) for estimating the target location in the second scenario. Using computer simulations, the performance of our methods was compared with the Cramer–Rao lower bound (CRLB) and it was shown that the proposed scheme outperforms conventional AOA-only measurement methods. Also, the effect of estimation error of parameter $n$ (which is related to the signal propagation path-loss exponent in the environment) on the performance of the proposed method was analyzed and it was concluded that it has no significant influence on the performance of the proposed method. Finally, the performance of the proposed method has been evaluated using the real received signal strength (RSS) data. [ABSTRACT FROM AUTHOR]

With the development of micro/nanoscale electromechanical systems and the wide applications of ultrashort pulse lasers, the classical and hyperbolic hygrothermal coupled models fail to predict the micro/nanoscale hygrothermoelastic responses. This paper presents a dual-phase-lag hygrothermal coupled model to analyze the transient responses of an infinitely long hollow cylinder subjected to hygrothermal loadings at the inner surface. By using the method of separating variables and the Laplace transform, the closed form solutions of temperature, moisture, displacement and stresses are obtained. The effects of the phase-lags of heat flux, moisture flux, temperature gradient and concentration gradient on the responses are calculated and displayed graphically. The present results are also compared with those based on the classical and hyperbolic models, which can be viewed as two special cases of the dual-phase-lag model. It can be shown that the phase-lags parameters play an essential role in controlling the heat and moisture transfer process. [ABSTRACT FROM AUTHOR]

The article focuses on a study that examines how the system of difference equations can be solved in the closed form. Topics discussed include system of difference equation, asymptotic behavior, closed form solution; employing appropriate transformation reducing the equation into linear difference equation of order-two; and obtaining the forbidden set of the initial values.

A much enhanced -with respect to existing literature- analytical model for FRCM coupons subjected to standard tensile tests is proposed. One fourth of the coupon is idealized considering two layers, matrix and fiber, subjected to a uniaxial stress state, mutually interacting at the interface through tangential stresses. The matrix is assumed elastic-perfectly fragile and the fiber linear elastic. The shear stress-slip relationship at the interface is tri-linear, with the first phase elastic, the second exhibiting linear softening followed by a third phase at possible non-null residual strength. The longitudinal equilibrium equations written for the two layers, suitably re-arranged, allow deducing a field problem governed in the three phases by a single second order linear differential equation where the independent variable is the interface slip, with solution retrievable analytically. Since the location of the points where the interface is in the different phases is not a-priori known, a discretization with small length elements is adopted. For each element the solution of the field problem is known in closed form and the only variables to determine are the integration constants coming from the solution of the differential equation. After a standard assemblage, all constants are derived imposing the boundary conditions at the extremes of the elements, which depend on the state of cracking of the matrix layer. The model is validated against two sets of experimental data on coupons tested in two different University laboratories in Italy. A satisfactory predictivity of both the global and local behavior is found. [ABSTRACT FROM AUTHOR]

The main objective of this paper is finding new types of discrete transforms with tuning factor t. This is not only analogy to the continuous Laplace transform but gives discrete Laplace-Fibonacci transform (LFt). This type of Laplace-Fibonacci transform is not available in the continuous case. The LFt generates uncountably many outcomes when the parameter t varies on (0,∞). This possibility is not available in the existing Laplace transform. All the formulae and results derived are verified by MATLAB.

• Periodic and Nonperiodic Modes on Postbuckling and Nonlinear have been studied. • Closed from solutions for cosine and sine imperfection have been derived. • Effect of non-periodic imperfection has been investigated. • Numerical differential-integral quadrature method is compared by analytical method. • Numerical solution is adopted to investigate the effect of nonlinear elastic foundation. This manuscript presents the influence of periodic (sine and cosine) and nonperiodic imperfections modes on buckling, postbuckling and dynamics of beam rested on nonlinear elastic foundations. The geometric von Kármán nonlinear strains induced by mid-plane stretching is considered. So, the generated equation of motion of imperfect beam is obtained as nonlinear integro-partial-differential equation. Elastic cubic nonlinear and linear springs and shearing layer are proposed to model elastic medium around the imperfected beam. Numerical differential-integral quadrature method (DIQM) in combination with Newton's method are used to find buckling loads and modes of imperfect beam that described by nonlinear integro-differential equation. In linear vibration analysis, the problem is discretized by DIQM and solved as a linear eigenvalue problem. The closed form solutions for static response and linear vibration problem of imperfect beam are obtained. Excellent agreement is observed between proposed numerical and analytical solutions. The numerical results indicate that imperfection modes and its amplitude have a weighty influence on the buckling load, postbuckling configurations and natural frequencies. Finally, numerical results for clamped-clamped (C-C) and simply supported (SS-SS) beams with local (nonperiodic) imperfection modes are presented. [ABSTRACT FROM AUTHOR]

We consider a nonlinear boundary-value problem consisting in the determination of a function that is meromorphic in the upper half-plane, satisfies the homogeneous Hilbert boundary condition on the set L of n intervals of the real axis and has a given module on the set . This problem was stated and solved in Cherepanov. Cherepanov proved that the required solution with a given number and location of its interior zeros and poles and with integrable singularities at all endpoints of L exists if and only if n−1 solvability conditions are satisfied. We prove that this problem is unconditionally solvable. A particular solution, , is found in the class of meromorphic functions with a properly chosen location of n−1 zeros and poles. Namely, we have shown that these zeros and poles are defined as the solution of some solvable real analogue of the Jacobi inversion problem. A general meromorphic solution of the Cherepanov problem is obtained with the help of the particular solution . The problem of a possible decrease in the number of zeros and poles of the desired solution is investigated. [ABSTRACT FROM AUTHOR]