Additional Term Research Articles

Nonlinear fractional-order differential equations: New closed-form traveling-wave solutions

Abstract The fractional-order differential equations (FO-DEs) faithfully capture both physical and biological phenomena making them useful for describing nature. This work presents the stable and more effective closed-form traveling-wave solutions for the well-known nonlinear space–time fractional-order Burgers equation and Lonngren-wave equation with additional terms using the exp ( − Φ ( ξ ) ) (-\Phi (\xi )) expansion method. The main advantage of this method over other methods is that it provides more accuracy of the FO-DEs with less computational work. The fractional-order derivative operator is the Caputo sense. The transformation is used to reduce the space–time fractional differential equations (FDEs) into a standard ordinary differential equation. By putting the suggested strategy into practice, the new closed-form traveling-wave solutions for various values of parameters were obtained. The generated 3D graphical soliton wave solutions demonstrate the superiority and simplicity of the suggested method for the nonlinear space–time FDEs.

Dynamics and Stability of Double-Walled Carbon Nanotube Cantilevers Conveying Fluid in an Elastic Medium

The paper concerns the dynamics and stability of double-walled carbon nanotubes conveying fluid. The equations of motion adopted in the current study to describe the dynamics of such nano-pipes stem from the classical Bernoulli–Euler beam theory. Several additional terms are included in the basic equations in order to take into account the influence of the conveyed fluid, the impact of the surrounding medium and the effect of the van der Waals interaction between the inner and outer single-walled carbon nanotubes constituting a double-walled one. In the present work, the flow-induced vibrations of the considered nano-pipes are studied for different values of the length of the pipe, its inner radius, the characteristics of the ambient medium and the velocity of the fluid flow, which is assumed to be constant. The critical fluid flow velocities are obtained at which such a cantilevered double-walled carbon nanotube embedded in an elastic medium loses stability.

Some New Aspects of Quantum Gravity

We have proposed the quantization of the gravitational field in a synchronous reference frame taking as independent position fields, the six spatial components of the metric tensor. The Einstein-Hilbert Lagrangian is quadratic in the space time derivatives of these metric tensor components and hence in particular, the momentum fields become linear functions of the space-time derivatives of the position fields. It is this fact that gives a simple form to the Hamiltonian density of the gravitational field in a synchronous frame, this simple form of the Hamiltonian being a quadratic function of the momentum fields with a shift that is linear in the spatial derivatives of the metric, very much like the Hamiltonian of a non-relativistic particle moving in a vector potential. Differential equations for the gravitational field propagator are derived and we explain how approximations to this propagator can be derived and used to deduce the graviton propagator corrections caused by nonlinear interactions of the graviton field with itself. We explain how this corrected graviton propagator can be used to deduce how much mass the graviton acquires due to these self-interactions of cubic and higher order. We then consider the important problem involving the coupling of a nonlinear field theory described by its Lagrangian density to a quantum noisy bath and explain how the resulting Hamiltonian of the field plus bath can be used to derive the Hudson-Parthasarathy noisy Schrodinger equation (HPS) which is a quantum stochastic differential equation for the joint unitary evolution of the field interacting with the noisy bath. We explain this in the context of gravity coupled to a noisy bath like a noisy electromagnetic field. The HPS equation contains linear as well as quadratic terms in the white bath noise with the linear terms representing quantum annihilation and creation/quantum Brownian motion process differentials and the quadratic terms representing quantum conservation/Poisson processes differentials. Finally we explain how using Feynman path integrals for fields for evaluating the quantum effective action produced by higher order cumulants of the current field, we can calculate corrections to the quantum effective action produced by higher order cumulants of the current field and hence demonstrate how gauge symmetries of the classical action get broken when we pass over to the quantum effective action with additional symmetry breaking terms produced by the presence of higher order cumulants of the current. This kind of approximate symmetry breaking is known to give masses to massless particles or more generally, corrections to the masses of already massive particles and we illustrate this idea in the context of interactions of the gravitational field with a random electromagnetic field being regarded as the current. This interaction is the standard Maxwell action used in general relativity. The drawback of our approach to quantum gravity is that is its not diffeomorphic invariant since we have chosen our frame to be always synchronous. Further work on how one can incorporate interactions of the gravitational field with a random non-Abelian gauge field is in progress which becomes important because it generates non only quadratic but also cubic and fourth degree terms in the gauge field when it interacts with gravity.

Beyond change scores: Employing an improved statistical approach to analyze the impact of entry fitness on physical performance during British Army basic training in men and women.

The aim was to use a robust statistical approach to examine whether physical fitness at entry influences performance changes between men and women undertaking British Army basic training (BT). Performance of 2 km run, seated medicine ball throw (MBT) and isometric mid-thigh pull (MTP) were assessed at entry and completion of Standard Entry (SE), Junior Entry-Short (JE-Short), and Junior Entry-Long (JE-Long) training for 2350 (272 women) recruits. Performance change was analyzed with entry performance as a covariate (ANCOVA), with an additional interaction term allowing different slopes for courses and genders (p < 0.05). Overall, BT courses saw average improvements in 2 km run performance (SE: -6.8% [-0.62 min], JE-Short: -4.6% [-0.43 min], JE-Long: -7.7% [-0.70 min]; all p < 0.001) and MBT (1.0-8.8% [0.04-0.34 m]; all p < 0.05) and MTP (4.5-26.9% [6.5-28.8 kg]; all p < 0.001). Regression models indicate an expected form of "regression to the mean" whereby test performance change was negatively associated with entry fitness in each course (those with low baseline fitness exhibit larger training improvements; all interaction effects: p < 0.001, > 0.006), particularly for women. However, when matched for entry fitness, men displayed considerable improvements in all tests, relative to women. Training courses were effective in developing recruit physical fitness, whereby the level of improvement is, in large part, dependent on entry fitness. Factors including age, physical maturity, course length, and physical training, could also contribute to the variability in training response between genders and should be considered when analyzing and/or developing physical fitness in these cohorts for future success of military job-task performance.

Fluctuation-Based Adaptive Structured Pruning for Large Language Models

Network Pruning is a promising way to address the huge computing resource demands of the deployment and inference of Large Language Models (LLMs). Retraining-free is important for LLMs' pruning methods. However, almost all of the existing retraining-free pruning approaches for LLMs focus on unstructured pruning, which requires specific hardware support for acceleration. In this paper, we propose a novel retraining-free structured pruning framework for LLMs, named FLAP (FLuctuation-based Adaptive Structured Pruning). It is hardware-friendly by effectively reducing storage and enhancing inference speed. For effective structured pruning of LLMs, we highlight three critical elements that demand the utmost attention: formulating structured importance metrics, adaptively searching the global compressed model, and implementing compensation mechanisms to mitigate performance loss. First, FLAP determines whether the output feature map is easily recoverable when a column of weight is removed, based on the fluctuation pruning metric. Then it standardizes the importance scores to adaptively determine the global compressed model structure. At last, FLAP adds additional bias terms to recover the output feature maps using the baseline values. We thoroughly evaluate our approach on a variety of language benchmarks. Without any retraining, our method significantly outperforms the state-of-the-art methods, including LLM-Pruner and the extension of Wanda in structured pruning. The code is released at https://github.com/CASIA-IVA-Lab/FLAP.

Clay and organic compost as quality conditioners of a sandy soil in the brazilian semiarid

Due to natural and anthropic pressures of semiarid regions, like sandy texture, organic matter (OM) deficiency, water scarcity and inadequate management, we carried out an experiment under greenhouse conditions, to evaluate the effects of clay and OM addition on the quality of a sandy soil of the Brazilian semiarid. The experiment lasted 75 days, testing four clay contents (10 and 31% natural soils, 15% by clay addition to a sandy soil and 26% by mixing clay subsoil to a sandy topsoil) in the absence and presence of organic compost (7.5g.kg-1). For biological parameters, sorghum plants were used for biometric and mineral composition analysis, in addition to assessing microbial activity (BSR, MBC, and qCO2). The results showed significant differences in soil microporosity and total porosity; the field capacity and permanent wilting point correlated linearly with clay content and OM addition; potencial and exchangeable soil acidity decreased significantly in the presence of compost. Sorghum plants showed higher values of biometric attributes and lower levels of nutrients in the presence of compost. The microbial activity did not show significant differences in terms of clay content or compost addition. The cluster analysis correlated the mixed soils (26%) to the lowest clay content soil (10%), and the clay addition (15%) to the highest clay content soil (31%), showing potential as soil conditioner in association with compost, as it might promote changes in the soil quality properties of semiarid regions.

Abstract 7393: Tumor model to tumor treatment: Applying deep learning approaches to map multimodal data from cancer model systems to patients

Abstract Despite large-scale efforts to measure the effect of drug screens in cancer cell lines, mapping the effects of drugs to patient samples has been a challenge. Biological differences between cell lines and patients, such as lack of immune system or microbiome, in-vitro survival adaptations, and biases in measurement technologies create differences across sample modalities that can confound analysis including prediction with machine learning. In this work, we propose a multiway batch correction strategy to enable algorithmic prediction of tumor drug response across model systems and patient data.Recent advances in batch correction algorithms have been motivated by the need to correct for batch effects in single-cell omics and include diverse approaches such as variational autoencoders (VAEs) and generative adversarial networks (GANs). Given the successes of these generative deep learning methods in single cell sequencing analysis, we worked to employ similar approaches to correct large omics measurements across various cancer datasets. Here, we describe mapping of datasets from diverse data sources and model systems to the same space, so that a predictive model of drug response built in a system such as cell lines can be used in biologically relevant models such as organoids, patient derived xenografts, and tumor data. Specifically, we introduce a modified loss function in a VAE using cosine similarity distance to minimize the effect of different cancer model systems in predicting cancer types. We evaluate the method on standard data types for drug response prediction - gene expression, copy number variation, and protein abundance. For this method, the cosine similarity is added as an additional term to the VAE reconstruction and Kullback-Leibler divergence loss terms. This injects a quantification of the dissimilarity between the tumor and tumor model distributions into the backpropagation and gradient descent for updating the model parameters resulting in an encoded representation of the data where the effect of data source has been attenuated while preserving the phenotypic signal. We evaluate our approach for biological signal preservation while reducing model system-specific noise with logistic regression and Euclidean distance. Our results show that the proposed VAE can effectively correct for platform effects and improve the accuracy of downstream integrative analyses. This study has the potential to improve the accuracy and translatability of proteogenomic drug response studies. The proposed modified VAE could be used to correct for platform effects in a variety of datasets, including those from different studies, different platforms, and different cancer types. This could lead to new insights into cancer biology, calibration of cancer patient digital twins, and the development of new diagnostic and therapeutic strategies. Citation Format: Brian Karlberg, Raphael Kirchgaessner, Jeremy R. Jacobson, Kyle Ellrott, Sara J. Gosline. Tumor model to tumor treatment: Applying deep learning approaches to map multimodal data from cancer model systems to patients [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 7393.

New analytical wave structures of the (3+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(3+1)$$\\end{document}-dimensional extended modified Ito equation of seventh-order

Partial differential equations are frequently employed to depict issues arising across various scientific and engineering domains. Efforts have been made to analytically solve these equations, revealing shortcomings in some widely utilized methods, including modeling deficiencies and intricate solution processes. To address these limitations, diverse analytical methods have been explored. The Ito equation, introduced in 1980, underwent development, leading to the formulation of a fifth-order Ito equation. A seventh-order integrable (3+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(3+1)$$\\end{document}-dimensional extended modified Ito equation emerged by augmenting this equation with three additional terms. In this study, novel exact solutions for the equation, absent in existing literature, were derived using the extended hyperbolic function and modified Kudryashov methods. To scrutinize the dynamic behavior of these findings, we presented 3D, contour, and 2D visualizations of select solutions. The results showcase numerous new solutions, underscoring the reliability and efficacy of the employed methods.

Hard-magnetic soft magnetoelastic materials: Energy considerations

In the finite magnetoelastic deformation context, the Zeeman magnetic energy on its own is found to be inconsistent with the general theory of nonlinear magnetoelasticity. An appropriate additional term, depending on the definition of the reference configuration magnetization, is used to modify the total magnetoelastic energy to confer consistency. In particular, this confirms that the total Cauchy stress tensor is symmetric, in contrast to recent conclusions in the literature where the Zeeman magnetic energy was utilized.

End-time regularity theorem for Brakke flows

AbstractFor a general k-dimensional Brakke flow in $${\mathbb {R}}^n$$ R n locally close to a k-dimensional plane in the sense of measure, it is proved that the flow is represented locally as a smooth graph over the plane with estimates on all the derivatives up to the end-time. Moreover, at any point in space-time where the Gaussian density is close to 1, the flow can be extended smoothly as a mean curvature flow up to that time in a neighborhood: this extends White’s local regularity theorem to general Brakke flows. The regularity result is in fact obtained for more general Brakke-like flows, driven by the mean curvature plus an additional forcing term in a dimensionally sharp integrability class or in a Hölder class.

Derivation of extended-OBurnett and super-OBurnett equations and their analytical solution to plane Poiseuille flow at non-zero Knudsen number

In this work, we analyse wall-bounded flows in the continuum to transition regime with the help of higher-order transport equations (super-set of the Navier–Stokes equation). Towards this, we incorporate second-order in Knudsen number accurate terms in the single-particle distribution function, and with this complete representation, we first derive the second-order accurate extended-OBurnett (EOBurnett) and third-order accurate super-OBurnett (SOBurnett) equations. We then demonstrate that these newly derived equations exhibit unconditional linear stability. We finally validate the equations by solving for plane Poiseuille flow and derive closed-form analytical solutions for the pressure and velocity fields. The pressure and velocity results thus obtained have been compared with direct simulation Monte Carlo (DSMC) data in the transition regime. The results from both the EOBurnett and SOBurnett equations are found to yield better agreement with DSMC data than that obtained from the Navier–Stokes equations. This improved agreement is attributed to the presence of additional terms in the proposed equations, which effectively capture the effect of the Knudsen layer near the wall. The obtained higher-order transport equations and the closed-form solution presented in this work are novel. The ability of the equations to describe the flow in the transition regime should form the basis for conducting further realistic analytical studies of wall-bounded flows in the future.

Adaptive Turbulence Model for Leading Edge Vortex Flows Preconditioned by a Hybrid Neural Network

Eddy-viscosity-based turbulence models provide the most commonly used modeling approach for computational fluid dynamics simulations in the aerospace industry. These models are very accurate at a relatively low cost for many cases but lack accuracy in the case of highly rotational leading edge vortex flows for mid to low aspect-ratio wings. An enhanced adaptive turbulence model based on the one-equation Spalart–Allmaras turbulence model is fundamental to this work. This model employs several additional coefficients and source terms, specifically targeting vortex-dominated flow regions, where these coefficients can be calibrated by an optimization procedure based on experimental or high-fidelity numerical data. To extend the usability of the model from single or cluster-wise calibrated cases, this work presents a preconditioning approach of the turbulence model via a neural network. The neural network provides a case-unspecific calibration approach, enabling the use of the model for many known or unknown cases. This extension enables aircraft design teams to perform low-cost Reynolds-averaged Navier–Stokes simulations with increased accuracy instead of complex and costly high-fidelity simulations.

Theoretical and numerical modeling of the effect of damage and dynamic strain aging on the plastic response of C45 steel alloys

A constitutive model for C45 steel alloys is proposed in this work by integrating the effect of damage and a specific phenomenon, so-called dynamic strain aging. For damage modeling, an energy-based isotropic damage model is implemented within a frame of continuum damage mechanics. The total stress is decomposed into athermal and thermal elements. The former includes the additional term for dynamic strain aging. This term is conceptually inspired by the probabilistic nature of dynamic strain aging, and its derivation is micromechanics-based. Both athermal and thermal components are defined as a function of temperature, equivalent plastic strain, and equivalent plastic strain rate because the occurrence and characteristics of dynamic strain aging are dependent on these factors. A finite element solution for the developed model is addressed additionally to further investigate the characteristics of plastic-damage behaviors and dynamic strain aging. The numerical results are compared to the experiments and theoretical predictions for its validation. The modified model developed in this work has largely reduced the number of fitting parameters compared to the previous model originally developed by the authors in 2019. Nevertheless, predictions from the proposed model still capture the experimental data accurately.

Дополнение к терминологическому словарю по морфологии диатомовых водорослей

This article is an addition to the glossary that was published by Gogorev et al. (2018). It includes more than 80 additional terms used to describe the morphology of diatoms that were either not included previously or definitions that have been corrected and clarified. The addition includes terms and their definitions in both Russian and English, as well as the corresponding terms in Latin.

Existence of non-exotic traversable wormholes in squared trace extended gravity theory

An extended gravity theory is used to explore the possibility of non-exotic matter traversable wormholes. In the extended gravity theory, additional terms linear and quadratic in the trace of the energy momentum tensor are considered in the Einstein-Hilbert action. Obviously, such an addition leads to violation of the energy-momentum tensor. The model parameters are constrained from the structure of the field equations. Non-exotic matter wormholes tend to satisfy the null energy conditions. We use two different traversable wormhole geometries namely an exponential and a power law shape functions to model the wormholes. From a detailed analysis of the energy conditions, it is found that, the existence of non-exotic matter traversable wormholes is not obvious in the model considered and its possibility may depend on the choice of the wormhole geometry. Also, we found that, non-exotic wormholes are possible within the given squared trace extended gravity theory for a narrow range of the chosen equation of state parameter.

A meta-analysis of the relationship between milk protein production and absorbed amino acids and digested energy in dairy cattle

Milk protein production is the largest draw on AA supplies for lactating dairy cattle. Prior NRC predictions of milk protein production have been absorbed protein (MP)-based and used a first-limiting nutrient concept to integrate the effects of energy and protein, which yielded poor accuracy and precision (root mean squared error [RMSE] >21%). Using a meta-data set gathered, various alternative equation forms considering MP, absorbed total EAA, absorbed individual EAA, and digested energy (DE) supplies as additive drivers of production were evaluated, and all were found to be superior in statistical performance to the first limitation approach (RMSE = 14%-15%). Inclusion of DE intake and a quadratic term for MP or absorbed EAA supplies were found to be necessary to achieve intercept estimates (nonproductive protein use) that were similar to the factorial estimates of the National Academies of Sciences, Engineering, and Medicine (2021). The partial linear slope for MP was found to be 0.409, which is consistent with the observed slope bias of -0.34 g/g when a slope of 0.67 was used for MP efficiency in a first-limiting nutrient system. Replacement of MP with the supplies of individual absorbed EAA expressed in grams per day and a common quadratic across the EAA resulted in unbiased predictions with improved statistical performance as compared with MP-based models. Based on Akaike's information criterion and biological consistency, the best equations included absorbed His, Ile, Lys, Met, Thr, the NEAA, and individual DE intakes from fatty acids, NDF, residual OM, and starch. Several also contained a term for absorbed Leu. These equations generally had RMSE of 14.3% and a concordance correlation of 0.76. Based on the common quadratic and individual linear terms, milk protein response plateaus were predicted at approximately 320 g/d of absorbed His, Ile, and Lys; 395 g/d of absorbed Thr; 550 g/d of absorbed Met; and 70 g/d of absorbed Leu. Therefore, responses to each except Leu are almost linear throughout the normal in vivo range. De-aggregation of the quadratic term and parsing to individual absorbed EAA resulted in nonbiological estimates for several EAA indicating over-parameterization. Expression of the EAA as g/100 g total absorbed EAA or as ratios of DE intake and using linear and quadratic terms for each EAA resulted in similar statistical performance, but the solutions had identifiability problems and several nonbiological parameter estimates. The use of ratios also introduced nonlinearity in the independent variables which violates linear regression assumptions. Further screening of the global model using absorbed EAA expressed as grams per day with a common quadratic using an all-models approach, and exhaustive cross-evaluation indicated the parameter estimates for BW, all 4 DE terms, His, Ile, Lys, Met, and the common quadratic term were stable, whereas estimates for Leu and Thr were known with less certainty. Use of independent and additive terms and a quadratic expression in the equation results in variable efficiencies of conversion. The additivity also provides partial substitution among the nutrients. Both of these prevent establishment of fixed nutrient requirements in support of milk protein production.

Predicting severe wildlife vehicle crashes (WVCs) on New Hampshire roads using a hybrid generalized additive model

Across the United States, wildlife vehicle crashes (WVCs) are increasing and remain consistently deadly to drivers, despite a downward trend in fatal automobile accidents overall. That said, the factors related to severe WVCs are unclear. With this in mind, we pursued a statistical model to reveal factors associated with WVCs that result in severe injury or death to drivers. We hypothesize that there are statistically significant interactions and non-linear relationships between these factors and severity occurrence. We developed a generalized additive model (GAM) with linear terms, additive terms, and a binary response for severity. We surmise that our fitted model results will quantify the relationship between significant variables and severity occurrence, and ultimately help to develop countermeasures to mitigate serious injury. The model was fitted to WVC records occurring between 2002 and 2019 in the state of New Hampshire. Fitted linear terms revealed: 1) in inclement weather, there is about a 22% increase in the odds of severity for slick surface conditions compared to dry surface conditions; 2) for the warmer months (spring/summer), there is a 42% decrease in the odds of severity for straight roads compared to those with curvature/incline; 3) for highways, the odds of severity decreases by 48% for accidents occurring on NH’s two major intestates highways, and 4) for spring/summer (as compared to the fall/winter), there is more than a 3-fold increase in the odds of severity for two-way traffic. Fitted additive terms revealed: 1) the odds of severity increased in the early hours, between midnight and 6AM, and after 5PM; 2) speeds between 45 and 60 mph are associated with an increase in the odds of a severe accident, while both lower and higher speeds (those below 45 and above 60 mph) are associated with a decrease in the odds of a severe accident; and 3) low, mid-range, and high human population densities are associated with decreases, increases, and decreases in odds of severity, respectively. Cross validation and resulting ROC curves gave evidence that our model is well specified and an effective predictor. Results could be used to inform drivers of potentially dangerous roadways/conditions/times.

On the emergent “Quantum” theory in complex adaptive systems

We explore the concept of emergent quantum-like theory in complex adaptive systems, and examine in particular the concrete example of such an emergent (or “mock”) quantum theory in the Lotka–Volterra system. In general, we investigate the possibility of implementing the mathematical formalism of quantum mechanics on classical systems, and what would be the conditions for using such an approach. We start from a standard description of a classical system via Hamilton–Jacobi (HJ) equation and reduce it to an effective Schrodinger-type equation, with a (mock) Planck constant ▪ , which is system-dependent. The condition for this is that the so-called quantum potential VQ, which is state-dependent, is canceled out by some additional term in the HJ equation. We consider this additional term to provide for the coupling of the classical system under consideration to the ‘environment’. We assume that a classical system could cancel out the VQ term (at least approximately) by fine tuning to the environment. This might provide a mechanism for establishing a stable, stationary states in (complex) adaptive systems, such as biological systems. In particular, we present a general argument as to why the non-equilibrium dynamics of a classical system could lead to a mock quantum description that ensures stability compatible with adaptability. In this context we emphasize the state dependent nature of the mock quantum dynamics and we also introduce the new concept of the mock quantum, state dependent, statistical field theory. We also discuss some universal features of the quantum-to-classical as well as the mock-quantum-to-classical transition found in the turbulent phase of the hydrodynamic formulation of our proposal. In this way we re-frame the concept of decoherence into the concept of ‘quantum turbulence’, i.e. that the transition between quantum and classical could be defined in analogy to the transition from laminar to turbulent flow in hydrodynamics.

Charged AdS black holes in presence of string cloud and Cardy-Verlinde formula

In this study, charged AdS black holes with a string cloud are taken into consideration. We identify three distinct black hole solutions within a specific temperature range, which subsequently merge into a single black hole beyond this range in the case of spherical space with low chemical potential and string density. However, in the case of large chemical potential and string density, only one black hole solution exists for all temperatures. Notably, we observe that for flat and hyperbolic space, there is only one black hole solution irrespective of the chemical potential and string density. By subtracting the contribution of the extremal black hole from the on-shell Euclidean action, the thermodynamical quantities associated with these black holes are calculated. We also investigate the stability of these black holes and find that medium-sized black hole is unstable. In the dual boundary theory side we verify the existence of bound state of quark-antiquark pair. Finally, we establish the Cardy-Verlinde formula for the boundary theory and we observed an additional energy term arising because of the presence of string cloud.

Nonlinear Robust Adaptive Control of Universal Manipulators Based on Desired Trajectory

The introduction of a dynamic model in robot trajectory tracking control design can significantly improve its trajectory tracking accuracy, but there are many uncertainties in the robot dynamic model which can be dealt with through robust control and adaptive control. The prevailing robust control as well as adaptive control methods require real-time computation of robot dynamics, but the extreme complexity of the robot dynamics equations makes it difficult to apply these methods in real industrial systems. To this end, this article proposes a robust adaptive control method based on the desired trajectory, which uses the desired trajectory to compute most of the control terms offline, including the robot’s nominal dynamics and regression matrices, and substantially reduces the need for real-time computation of the feedback signals. The robust term modifies the perturbation of the inertial parameters of the links, the adaptive term learns the friction coefficients of the joints online, and an additional compensation term is designed to satisfy the Lyapunov stability condition of the system. Finally, taking a universal manipulator as the experimental platform, the control performances of different control methods are compared to show the feasibility of the controller and the effective reduction in real-time computational complexity.