Endpoint Conditions Research Articles

Computation of eigenfunctions and eigenvalues for the Sturm–Liouville problem with Dirichlet boundary conditions at the left endpoint and Neumann conditions at the right endpoint

A functional-based variational method is proposed for finding the eigenfunctions and eigenvalues in the Sturm–Liouville problem with Dirichlet boundary conditions at the left endpoint and Neumann conditions at the right endpoint. Computations are performed for three potentials: sin((x–π)2/π), cos(4x), and a high nonisosceles triangle.

A Synergetic Brain-Machine Interfacing Paradigm for Multi-DOF Robot Control

This paper proposes a novel brain-machine interfacing (BMI) paradigm for control of a multijoint redundant robot system. Here, the user would determine the direction of end-point movement of a 3-degrees of freedom (DOF) robot arm using motor imagery electroencephalography signal with co-adaptive decoder (adaptivity between the user and the decoder) while a synergetic motor learning algorithm manages a peripheral redundancy in multi-DOF joints toward energy optimality through tacit learning. As in human motor control, torque control paradigm is employed for a robot to be adaptive to the given physical environment. The dynamic condition of the robot arm is taken into consideration by the learning algorithm. Thus, the user needs to only think about the end-point movement of the robot arm, which allows simultaneous multijoints control by BMI. The support vector machine-based decoder designed in this paper is adaptive to the changing mental state of the user. Online experiments reveals that the users successfully reach their targets with an average decoder accuracy of over 75% in different end-point load conditions.

Probability-Based Design of Experiments for Batch Process Optimization with End-Point Specifications

Consistently complying with end-point specifications, mainly end-use product properties, is a key issue to the competitiveness of batch processes. To maximize in some way the probability of observing successful runs, a series of experiments is specifically designed to pinpoint the smallest operating region that guarantees that end-point conditions can meet their desired targets. On the basis of data-driven modeling of the underlying binomial probability of success, the proposed methodology seeks to trade off improving parameter precision with experimenting in a reduced region where there is a high probability of satisfying end-point specifications. Two case studies are used to demonstrate the efficacy of the probability-based optimal design of experiments to find optimal policies for runs involving stochastic binary outcomes. Run-to-run improvement of the success rate for the operating policy in the acetoacetylation of pyrrole with diketene is first discussed. Results obtained for emulsion polymerization ...

An optimal integral sliding mode control strategy based on a pseudospectral method for a class of affine systems

This paper presents an optimal integral sliding mode control method based on a pseudospectral method for a class of affine systems with state and control constraints. First, a general form of an integral sliding mode is presented. Integral sliding mode control cannot deal with the problem of states and control constraints, nor can it satisfy the minimization of the cost function. The pseudospectral method has a high convergence speed and performs well in solving optimal control problems with general performance index, endpoint conditions and path constraints. In consideration of these advantages, an optimal integral sliding mode controller is determined by the pseudospectral method. Then, the stability analysis of optimal pseudospectral sliding mode method is discussed. Finally, numerical simulations show the effectiveness of the proposed method. An application example, consisting of an overhead crane system, is investigated to demonstrate the effectiveness and robustness of the proposed technique.

A Generic Storage Model Based on a Future Cost Piecewise-Linear Approximation

This paper presents a generic storage model (GSM) inspired by the scheduling of hydraulic reservoirs. The model for steady state short-term operational studies interlaces with the long-term (LT) energy scheduling through a piecewise-linear future cost function (FCF). Under the assumption that a stochastic dual dynamic programming approach has been used to solve the energy schedule for the LT, the FCF output from that study will be processed to obtain an equivalent marginal opportunity cost for the storage unit. The linear characteristic of a segment of the FCF will allow a linear modeling of the storage unit production cost. This formulation will help to coordinate the renewable resource along with storage facilities in order to find the optimal operation cost while meeting end-point conditions for the LT plan of the energy storage. The generic model will be implemented to represent a battery storage and a pumped-hydro storage. A stochastic unit commitment with the GSM will be formulated and tested to assess the day-ahead scheduling strategy of a virtual power plant facing uncertainties from production, consumption, and market prices.

Molecular Evidence of Ongoing Antigen Driven Somatic Hypermutation in the Natural History of Classic and Variant Hairy Cell Leukemia

Classic hairy cell leukemia (HCL) is a clonal chronic B-cell malignancy representing 2% of all leukemias, with neoplastic B lymphocytes in the blood, bone marrow and organs of the classic reticuloendothelial system. HCL variant (HCLv) is less common, typically has inferior prognosis, and usually lacks several HCL-related features including BRAF V600E, CD25, and Annexin A1. The malignant cells in HCL and HCLv patients have one or in unusual cases two different functional immunoglobulin heavy chain rearrangements. Significant variability can be observed in the 3rd complementarity determining region (CDR3), comprising the variable heavy (IGHV), diversity (IGHD), and joining (IGHJ) domains. A role for continued antigen selection in the pathogenesis and evolution of HCL and HCLv has been suggested but limited evidence has been found.We examined HCL and HCLv-derived IGHV genes by massive parallel deep sequencing in 15 HCL and 7 HCLv cases. In all studied samples, a productive monoclonal tumor-derived IGH sequence was detected. Analysis of all reads sharing clonal CDR3 motifs revealed the existence of dominant subclone expansion and multiple subclonal variants. Analysis of phylogenetic trees indicated multiple branching and therefore exposure to multiple rounds of somatic hypermutation (SHM) in the evolution of clonally-related malignant cells. To investigate a possible cause of the high SHM activity and the large number of subclones in HCL and HCLv, we studied the expression of activation induced cytidine deaminase (AID), an enzyme essential for somatic hypermutations, expressed by germinal center (GC) B-cells where SHM occurs. In 5 HCL and 3 HCLv cases we detected a high expression level of AID mRNA, including wild-type and 2 splice variants; in 10 HCL, 4 HCLv, and 3 normal peripheral blood samples, AID expression was not detected using standard end-point PCR conditions. However, more sensitive real-time quantitative PCR detected AID transcripts in virtually all tested HCL and HCLv cases, although the range of transcript levels was large between different cases and varied with individual cases over time.The data obtained for both HCL and HCLv fit a model of tumorigenesis in which the BRAF V600E mutation (or another event in HCLv) initiates neoplastic transformation in a GC B-cell committed to terminal differentiation, but still thereafter still targeted by ongoing SHM DisclosuresNo relevant conflicts of interest to declare.

Non-Gaussian Bridge Sampling with an Application

This paper provides a new bridge sampler that can efficiently generate sample paths, subject to some endpoint condition, for non-Gaussian dynamic models. This bridge sampler uses a companion pseudo-Gaussian bridge as the proposal and sequentially re-simulates sample paths via a sequence of tempered importance weights in a way bearing resemblance to the density-tempered sequential Monte Carlo method used in the Bayesian statistics literature. This bridge sampler is further accelerated by employing a novel idea of k-fold duplicating a base set of sample paths followed by support boosting. We implement this bridge sampler on a GARCH model estimated to the S&P 500 index series, and our implementation covers both parametric and non-parametric conditional distributions. Our performance study reveals that this new bridge sampler is far superior to either the simple-rejection method when it is applicable or other alternative samplers designed for paths with a fixed endpoint. Computing SRISK of the NYU-Stern Volatility Institute is then used to demonstrate the method's real-life applicability.

Property (D) and the Lavrentiev phenomenon

In 1926 Lavrentiev gave an example of a free problem in the calculus of variations for which the infimum over the class of functions in satisfying prescribed endpoint conditions was strictly less than the infimum over the dense subset of admissible functions in . This property is now referred to as the Lavrentiev phenomenon. After Lavrentiev’s discovery, Tonelli and Mania gave sufficient conditions under which this phenomenon does not arise. After these results, the study of the Lavrentiev phenomenon lay dormant until the 1980s when a series of papers by Ball and Mizel and by Clarke and Vinter gave a number of new examples for which the Lavrentiev phenomenon occurred. Also in 1979, Angell showed that the Lavrentiev phenomenon did not occur if the integrands satisfy a certain analytic property known as property (D). Moreover, he showed that the conditions of Tonelli and Mania insured that the analytic property (D) was satisfied. Since Angell’s result there have been several papers that have discussed the nonoccurence of the Lavrentiev phenomenon for free problems in the calculus of variations. The purpose of this paper is twofold. First to present a general approach to the proofs of these later papers which unifies the results, and second to show that the extra conditions imposed on the integrands insure property (D) holds with respect to the relevant sequence.

An improved parameter identification schema for the dynamic model of LD converters

The process of conversion in Linz–Donawitz converters is a crucial stage in the production of steel: oxygen is blown on the surface of the melted bath in order to reduce the carbon concentration. At the same time, suitable amounts of coolants are added in order to govern the increase of the bath temperature and reduce the impurities (favoring the slag formation). The aim is to direct the bath of melted steel to the desired final condition, in terms of temperature and carbon content. At around 92–93% of the complete process of conversion, the oxygen blowing is suspended and the In-Blow is performed, i.e. a steel sample is collected by means of a lance introduced in the melted bath and its carbon percentage and temperature measured.A dynamic model, through two characteristic equations, describes the evolution of the carbon percentage and temperature of the melted steel during the final phase of the conversion process, i.e. from the In-Blow until the end. Based on this model, the volume of oxygen to be blown during this phase and the amount of coolant to be added in order to reach the required final (End-Point) conditions of carbon percentage and temperature can be calculated. The model is nonlinear and depends on four parameters to be estimated. Based on a dimensional analysis and on a large set of experimental data, the nominal model has been modified introducing the hypothesis that the parameters are not constant, but depend on the temperature. Within this framework the novel model is identified exploiting Least Squares (LS) methods and its output is compared with the existing practice.

Sex-Related Differences In Anticipatory Fatigue Prior To A Bout Of Treadmill Running

Subjective responses to exercise change with perceived demands, even within a single bout, and may be moderated by subject characteristics such as sex. Additionally, these perceptions and short-term memories they create may influence perception of time. PURPOSE: To determine whether running with or without a known endpoint has an effect on psychological responses to exercise and retrospective perception of time. METHODS: 22 experienced runners (11 men, 11 women) completed two conditions: 1) a run with an unknown endpoint distance (UNKN) relative to each subject’s running history; and 2) a run to the same distance with knowledge of the endpoint (KN). Subjects were able to self-pace but received no feedback (blind to speed, distance and elapsed time). They completed the Subjective Exercise Experience Scale (SEES) before, during and after exercise to assess Psychological Well Being (PWB), Psychological Distress (PD) and Fatigue (F). After each session, they were asked how long they felt it took to complete the distance. This time (in minutes:seconds) was compared to the actual time (time estimation ratio: TER). Paired samples t-tests were used to compare endpoint conditions in TER. Repeated-measures ANOVA with sex as a between-subjects factor was used to investigate differences between 2 conditions (UNKN, KN) and 3 time points (pre, during, post). RESULTS: There was no differences in TER between conditions (UNKN: 1.02±0.24, KN: 1.00±0.07; p=.676). There was a significant effect of time (p women; p=.016). There was a significant interaction between sex and endpoint condition (p=.033) for F, with no difference for men but significantly greater F before the unknown condition in women. CONCLUSIONS: We found differences in how men and women perceive a bout of exercise when the endpoint is not known and they are allowed to self-pace. Men showed more overall Psychological Distress. Women reported significantly more Fatigue before exercise compared to the men only in the unknown endpoint condition. Women in the study may have had more anxiety or anticipation of physical demands when they did not know when a bout of exercise would end.

The Effect of Endpoint Knowledge on Perceived Exertion, Affect, and Attentional Focus During Self-Paced Running

The purpose of this study was to determine the effect of endpoint knowledge on psychophysiological variables. Twenty-two runners (11 men and 11 women) participated in 2 conditions: a run with an unknown endpoint and a run to the same distance with knowledge of the endpoint. Rating of perceived exertion (RPE), affect, heart rate, and attentional focus were assessed during testing. Subjects ran faster when the endpoint was known (p < 0.01) but no differences in RPE, affect, or heart rate between conditions were present (p > 0.05). There were differences in attentional focus between conditions (p = 0.034) and subjects reported more associative thoughts in the known endpoint condition. Cardiorespiratory fitness was a significant predictor of attentional focus in the known endpoint condition. In sum, when the endpoint was known, subjects used more associative strategies as RPE increased, and those with higher fitness levels used more associative strategies overall.

One-Step Iteration Scheme for Multivalued Nonexpansive Mappings in CAT(0) Spaces

In this paper, we introduce one-step iteration scheme involving two multivalued nonexpansive mappings in CAT(0) spaces and utilize the same to prove Δ-convergence as well as strong convergence theorems with and without end point conditions. Our results generalize and extend several relevant results in the literature.

Stochastic Bridges of Linear Systems

We consider particles obeying Langevin dynamics while being at known positions and having known velocities at the two end-points of a given interval. Their motion in phase space can be modeled as an Ornstein-Uhlenbeck process conditioned at the two end-points-a generalization of the Brownian bridge. Using standard ideas from stochastic optimal control we construct a stochastic differential equation (SDE) that generates such a bridge that agrees with the statistics of the conditioned process, as a degenerate diffusion. Higher order linear diffusions are also considered. In general, a time-varying drift is sufficient to modify the prior SDE and meet the end-point conditions. When the drift is obtained by solving a suitable differential Lyapunov equation, the SDE models correctly the statistics of the bridge. These types of models are relevant in controlling and modeling distribution of particles and the interpolation of density functions.

A new iteration scheme for a hybrid pair of generalized nonexpansive mappings

Abstract In this paper, we construct an iteration scheme involving a hybrid pair of nonexpansive mappings and utilize the same to prove some convergence theorems. In the process, we remove a restricted condition (called end-point condition) in Sokhuma and Kaewkhao’s results (Fixed Point Theory Appl. 2010:618767, 2010). Thus, our results generalized and improved several results contained in Sokhuma and Kaewkhao (Fixed Point Theory Appl. 2010:618767, 2010), Akkasriworn et al. (Int. J. Math. Anal. 6(19):923-932, 2012), Uddin et al. (Bull. Malays. Math. Soc., accepted) and Sokhuma (J. Math. Anal. 4(2):23-31, 2013). MSC:47H10, 54H25.

Restoration for the Future: Endpoints, Targets, and Indicators of Progress and Success

Setting endpoints and targets in forest restoration is a complicated task that is best accomplished in cooperative partnerships that account for the ecology of the system, production of desired ecosystem goods and services, economics and well-being of society, and future environments. Clearly described and quantitative endpoints and intermediary targets are needed to manage restoration of ecosystem structure, composition, function, and production. Selecting indicators of key ecosystem attributes that are linked to endpoint and target condition, function, sustainability, health, integrity, resilience, and production is important to monitoring restoration success. Indicators are used to track ecosystem trajectory, assess progress toward achieving endpoints and targets, adapt management, and communicate with external publics. Reference sites can be used to help set endpoints and targets with caution. Other science-based ecosystem models or management tools are available to help quantify intermediate targets and endpoints. Continued work to better understand historic ecosystem conditions is fundamental to assessing change, extent of damage, and restoration potential. A hierarchy of forest plans from regional and landscape to site specific are useful for defining endpoints, targets, and indicators at appropriate ecological scales; and to consider populations, ecosystem function, and socioeconomic factors that operate at a variety of scales.

Solvability of a theory of anti-plane shear with partially coated boundaries

We consider the anti-plane shear of an elastic solid whose boundary is partially reinforced by a thin solid film represented by the union of a finite number of open curves. The solvability of the resulting boundary value problems is complicated by the presence of end-point conditions which must be satisfied at the ends of each section of the reinforcing film. In order to avoid complicated solvability conditions which carry no clear physical meaning, we modify the boundary integral equation method using an equivalent (lower-order) reinforcement condition which leads to the desired solvability results for the corresponding boundary value problems.

Stability of a turnpike phenomenon for approximate solutions of nonautonomous discrete-time optimal control systems

We study turnpike properties of approximate solutions of nonautonomous discrete-time optimal control systems which are determined by sequences of lower semicontinuous objective functions. To have these properties means that the approximate solutions of the problems are determined mainly by the objective functions, and are essentially independent of the choice of intervals and endpoint conditions, except in regions close to the endpoints. We show that these turnpike properties are stable under small perturbations of the objective functions.

Turnpike properties of approximate solutions of dynamic discrete time zero-sum games

We study existence and turnpike properties of approximate solutions for a class of dynamic discrete-time two-player zero-sum games without using convexity-concavity assumptions. We describe the structure of approximate solutions which is independent of the length of the interval, for all sufficiently large intervals and show that approximate solutions are determined mainly by the objective function, and are essentially independent of the choice of interval and endpoint conditions.

Two-point free energy distribution function in (1+1) directed polymers

In this brief communication it is demonstrated how by using the Bethe ansatz technique the explicit expression for the two-point free energy distribution function in (1+1) directed polymers with fixed end-point boundary conditions can be derived in a rather simple way. The obtained result is equivalent to the one previously derived by Prolhac and Spohn (2011 J. Stat. Mech. P01031).

Rapid Stabilization for a Korteweg-de Vries Equation From the Left Dirichlet Boundary Condition

This paper deals with the stabilization problem for the Korteweg-de Vries equation posed on a bounded interval. The control acts on the left Dirichlet boundary condition. At the right end-point, Dirichlet and Neumann homogeneous boundary conditions are considered. The proposed feedback law forces the exponential decay of the system under a smallness condition on the initial data. Moreover, the decay rate can be tuned to be as large as desired. The feedback control law is designed by using the backstepping method.