One-sided Solutions Research Articles

Problems and Prospects for a One-Sided Solution to Kripke’s Problem

This text is a replica of the article by E.V. Borisov А Straight Solution to Kripke’s problem. The proposed solution to the problem of skepticism regarding the meaning of a linguistic expression is based on the idea of language and speech activity, limited to the act of use. Such a truncated and one-sided version of the analysis of language presents a picture where the only subject capable of understanding the meanings of words is the speech agent himself. Although this approach partially allows us to resolve the skeptical problem, it arises again when we pay attention not to the agent of speech, but to the recipient to whom speech activity is directed.

A note on one-sided solutions for optimal stopping problems driven by Lévy processes

All optimal stopping problems with increasing, logconcave and right-continuous reward functions under Lévy processes have been shown to admit one-sided solutions. There is relatively little research attention, however, on constructing an explicit solution of the problem when the reward function is increasing and logconcave. Thus, this paper aims to explore the role of the monotonicity and logconcavity in the characterization of the optimal threshold value, particularly in terms of the ladder height process. In this paper, with additional smoothness assumptions on the reward function, we give an explicit expression for the optimal threshold value provided that the underlying Lévy process drifts to −∞ almost surely. In the particular case where the reward function is (x+)ν=(max{x,0})ν, ν∈(0,∞), we establish a connection indicating that the expression coincides with the positive root of the associated Appell function.

General optimal stopping with linear cost

This article treats both discrete time and continuous time stopping problems for general Markov processes on the real line with general linear costs as they naturally arise in many problems in sequential decision making. Using an auxiliary function of maximum representation type, conditions are given to guarantee the optimal stopping time to be of threshold type. The optimal threshold is then characterized as the root of that function. For random walks, our results condense in the fact that all combinations of concave increasing payoff functions and convex cost functions lead to a one-sided solution. For Lévy processes, an explicit way to obtain the auxiliary function and the threshold is given by use of the ladder height processes. Lastly, the connection from discrete and continuous problems and possible approximation of the latter via the former is discussed and the results are applied to sequential tests of power one.

Multicriteria Competitive Games as Models in Operations Research

The problem of a priori estimation of the result of a mulicriteria two-person competitive game is considered in the framework of operations research. Various aspects of decision making in such games are discussed. Relations between the values of a vector best guaranteed result (BGR) for both players are obtained. The difference of the mulicriteria antagonistic game considered as a model of taking into account the natural uncertainty from the mulicriteria zero-sum game considered as interaction with a purposeful opponent is formalized. Special attention is paid to the concepts of the value and solution of the latter game. As the basic solution of this game, we use the multicriteria Shapley equilibrium when it gives to each player the result not worse than her or his BGR. It is shown that the last condition is not restrictive. The definition of the one-sided value of the multicriteria game as the player’s BGR if her BGR is independent of the order of the players' moves and the definition of the corresponding one-sided solution are given. It is proved that the equilibrium is weaker than the one-sided solution, and the equilibrium always exists in mixed strategies. The existence of a one-sided solution in mixed strategies is guaranteed by a special interpretation of multicriteria averaging. To justify the conclusions, Slater’s value of the multicriteria optimum is parameterized using Germeier’s scalarizing function.

Blue–green architecture: A case study analysis considering the synergetic effects of water and vegetation

Blue–green infrastructure is a network of natural and near-natural areas that has a positive effect on the quality of urban environment. This multifunctional planning approach addresses different issues and objectives depending on whether the focus is on the blue (water) or the green (vegetation) elements. Green-motivated projects aim to densify urban vegetation and include the growing sector of building greening. A good climatic effect of vegetation can be achieved by sufficient irrigation. In many cases, this approach results in additional water requirements. Blue-motivated projects consider water accumulation in cities (e.g., by heavy rainfall) as a waste product and look for solutions for local drainage and evaporation. These planning approaches offer only one-sided solutions and create no sufficient interfaces between water availability and water demand. Based on four case studies, this work examines the extent to which blue–green projects take advantage of the possibilities for the synergetic use of resources. The projects are analyzed graphically by applying the daily tools of architects as a scientific method. A graphic presentation of the blue and green components makes existing solutions and missing links visible. Analytical results show that buildings can be considered to be an interface for blue–green systems. Moreover, the possible synergies are often overlooked during the planning process. This fact highlights the need for a new planning approach that interlinks blue and green aspects that are already in the early planning stages.

Better Positioned to Teach the Rules than to Change Them: University Actors in Two Low-Income, First-Generation Student Support Programs

ABSTRACTLow-income, first-generation (LIFG) students complete college at disproportionately low rates. This qualitative study examines this gap from the perspective of university actors who directly support LIFG students in two student support programs at one public university. Drawing on in-depth interviews and observations, this study investigates how these actors conceptualize the problems that LIFG students face, the solutions that will yield success, and their work in relation to the wider goals of the university. The researcher finds that program staff and mid-level administrators have a deep understanding of the barriers that LIFG students face in mastering the rules of the academic field and the high costs when they fail. While both programs identify six common barriers to success, three structural and three individual, the programs work to mitigate only individual barriers. This one-sided solution reflects the staff and administrators’ own position within the academic social field; they do not have enough social, economic, or symbolic capital to enact structural changes within the university and feel largely powerless to change the inequitable rules of the game. This paper concludes with recommendations for future research and institutional efforts to support the success of LIFG students.

One-sided solutions for optimal stopping problems with logconcave reward functions

AbstractIn the literature on optimal stopping, the problem of maximizing the expected discounted reward over all stopping times has been explicitly solved for some special reward functions (including (x+)ν, (ex − K)+, (K − e− x)+, x ∈ ℝ, ν ∈ (0, ∞), and K > 0) under general random walks in discrete time and Lévy processes in continuous time (subject to mild integrability conditions). All such reward functions are continuous, increasing, and logconcave while the corresponding optimal stopping times are of threshold type (i.e. the solutions are one-sided). In this paper we show that all optimal stopping problems with increasing, logconcave, and right-continuous reward functions admit one-sided solutions for general random walks and Lévy processes, thereby generalizing the aforementioned results. We also investigate in detail the principle of smooth fit for Lévy processes when the reward function is increasing and logconcave.

A general method for finding the optimal threshold in discrete time

ABSTRACTWe develop an approach for solving one-sided optimal stopping problems in discrete time for general underlying Markov processes on the real line. The main idea is to transform the problem into an auxiliary problem for the ladder height variables. In case that the original problem has a one-sided solution and the auxiliary problem has a monotone structure, the corresponding myopic stopping time is optimal for the original problem as well. This elementary line of argument directly leads to a characterization of the optimal boundary in the original problem. The optimal threshold is given by the threshold of the myopic stopping time in the auxiliary problem. Supplying also a sufficient condition for our approach to work, we obtain solutions for many prominent examples in the literature, among others the problems of Novikov-Shiryaev, Shepp-Shiryaev, and the American put in option pricing under general conditions. As a further application we show that for underlying random walks (and Lévy processes in continuous time), general monotone and log-concave reward functions g lead to one-sided stopping problems.

Convergence and applications of some solutions of the confluent Heun equation

We study the convergence of a group of solutions in series of confluent hypergeometric functions for the confluent Heun equation. These solutions are expansions in two-sided infinite series (summation from minus to plus infinity) which are interpreted as a modified version of expansions proposed by Leaver (1986). We show that the two-sided solutions yield two nonequivalent groups of one-sided series solutions (summation from zero to plus infinity). In the second place, we find that one-sided solutions of one of these groups can be used to solve an equation which describes a time-dependent two-level system of Quantum Optics. For this problem, in addition to finite-series solutions, we obtain infinite-series wavefunctions which are convergent and bounded for any value of the time t, and vanish when t goes to infinity.

Optimal Stopping for Lévy Processes with One-Sided Solutions

An explicit solution of an infinite horizon optimal stopping problem for a Levy process with a nonmonotonic reward function is given, in terms of the overall supremum of the process, when the solution of the problem is one-sided. The results are obtained via the consideration of the generalized averaging function associated with the problem. The method, initially tailored to handle polynomial rewards, has a wide range of applications, as shown in the examples: optimal stopping problems for general polynomial rewards of degree two and three for spectrally negative processes, a quartic polynomial reward and Kou's process, a portfolio of call options, and a trigonometric payoff function. These last two examples are given for general Levy processes.

Introduction

In this collection, we examine the application of the ecological model in prevention programs. A review of the literature presents a historical account of the development of the model and provides a basis for the rationale behind its use. Four empirical articles then provide a method for measuring the application of an ecological framework in program design and implementation, and evaluations of programs using components of the model. We conclude that ecological programming, while popular in rhetoric, is complex in both its design and implementation. Ecological approaches show merit over one-sided solutions, but need further investigation to show when these are the most efficacious approach and when only limited adherence is optimal.

Tokamak edge electron diffusion and distribution function in the lower hybrid antenna electric field

Comprehensive test electron simulations supported by theory are carried out to determine the diffusion and distribution function of tokamak edge electrons interacting with the lower hybrid (LH) grill electric field. Edge electrons respond to the antenna field by diffusing in velocity space within a region of overlapping LH grill spectrum Fourier modes, and streaming along magnetic field lines in both directions away from the LH grill. The intrinsic electron stochasticity induced by the grill field depends here not only on field strength but also on electron velocity. Electron velocity phases between successive scattering events on wave-guides are thereby strongly correlated with the result that after an initial quasi-linear rise the electron mean velocity and variance show a tendency to saturate and the diffusion coefficient decreases along the grill. The diffusive electron response in velocity space permits the representation of the LH field effect by a Langevin stochastic process, based upon a diffusion coefficient derived herein. Results from corresponding Monte Carlo calculations agree with simulation results which use the full radio-frequency-induced electron trajectories. The rapid radio-frequency timescale ≈1/ωLH in the problem can be thus replaced by the much slower electron transit time across a wave-guide. This gives here a reduction of about ten in CPU time. We also analytically find one-sided solutions of the diffusion electron kinetic equation under thermal Maxwellian boundary conditions imposed at either grill end, describing the two counter-propagating electron populations resonant with the grill spectrum.

Decision rights, residual claim and performance: A theory of how the Chinese state enterprise reform works

This paper is intended to model the process of shifting decision rights and residual claim from the central agent (government) to the inside members of the firm in China, and to analyze how the reform has improved performance of the state-owned enterprises. We show that the bargaining solution between the central agent and the firm is preferred to a one-sided solution, and that managerial discretion of state enterprises can greatly improve efficiency through both its direct incentive effect and indirectly hardening budget constraints. Further improvement of efficiency requires that authority of selecting management is transferred from bureaucrats to capitalists, which implies privatization of the state enterprises. China is already well on its way.

The Question of Determinism in Relations Between Natural Environment and Society

The paper analyses the main tendencies existing in the relation between natural environment and the moves of society. The author stresses the fact that the solution of the problem has been hindered up to now by two extremes: the geographical determinism and indeterminism. Geographical determinism mostly concentrated upon its historical importance and social function, meanwhile gnoseological analysis was completely missing. The analysis - carried out by the author - shows that the seemingly definite term may indicate several different kinds of determinism, from mechanical causality to some very uncertain and problematic conditioning. The fact that geographical determinism cannot hold out theoretically is no reason why the scientific determinism should be completely substituted by indeterminism as was the practice recently. Indeterminism is only the other extreme. Only recently, in unfavourable reflected in the economic practice of the socialistic states. Through the analysis of indeterministic tendencies, the author in several geographical articles shows that this conception is not dialectical at all, and gives a clear definition of the relation between the society and nature. The only acceptable supposition is the one based upon the dialectical- materialistic philosophy. It highly surpasses both above-mentioned extremes and enables the only real, i. e. not one-sided solution.

The radiation balance of slopes

The radiation balance problenl, at present, has rather a poor and one-sided solution. Only the inflow of direct solar radiation to differently oriented slopes has been closely studied. The precise theoretical formula has been derived for determining the flux of direct solar radiation to slopes of different exposure; numerous calculations, tables, and nomograms for defining the irradiation of slopes with direct solar radiation are being carried out by various workers. The nature of the flux of scattered and reflected radiation to the slopes and the effective long-wave radiation of the slopes have scarcely been investigated; such studies have been reviewed (1, 2, 3). The computation of scattered and reflected radiation fluxes to the slopes as well as the effective radiation of the slopes is rather complicated owing to the fluxes being considerably non-isotropic. As a rule, the radiation is assumed to be in all cases where practical calculations of the scattered and reflected radiation to the slopes are involved, simple formulae expressing the components of the slope radiation balance being derived with the help of the corresponding components of the radiation balance of a horizontal surface. However, it is not ascertained in what cases and with what accuracy the isotropic approximation can be valid. The fluxes of scattered and reflected radiation to the slopes and the effective radiation of the slopes can be exactly determined either by measuring them for each specific slope, or by calculating the radiation influx to the slopes according to the given angular distribution of the radiation intensity. If the angular distribution of the scattered radiation to the slope is known, the flux of this scattered radiation can be estimated from the following exact formula: