Analysis of Bus Fare Structure to Observe Modal Shift, Operator Profit, and Land-Use Choices through Combined Unified Transport Model

In order to design sustainable urban transport systems, the inclusion of the behaviors of different stakeholders is imperative. In this study, we formulated the interactions of behaviors between transport operator, landowner, workplace, residence, route and mode choices, and location of firms and businesses through a combined unified model of land-use and transport system. The commuters have two mode choices for traveling: private car and public bus. They are inclined to choose a transit mode with minimum traveling costs. We combined two models, maximization of operator profit constrained by bus frequency, while maintaining the formulation of other stakeholders through an assignment sub-model. The resulting formulation is bi-level, which is optimally solved for a small-sized instance containing two zones. The findings suggest that if the bus fare is reduced, the demand of public bus is increased. However, the operators’ profit is optimized within a certain range of fares and is lowered when the fare is too low or too high. It is determined that maximum bus frequency does not guarantee maximum profit to the service operator. The impacts of traveling costs on residence choice behavior suggest that if link fares are more, many of people opt not to travel between different zones. The analysis results presented in this paper are calculated for two types of link fares: a fixed fare (30 currency), and a range of link fare (5 to 100 currency). Different variants of the same formulation can be applied for real settings to better comprehend the nature of the model and its applications.

Finding the fundamental solution of the bi-axially symmetric Laplace–Beltrami equation using generalized shift operator

Many physical processes are described by partial differential equations. The relevance of this study is due to the need to solve applied problems of quantum mechanics, the theory of elasticity, and heat capacity. In this paper, an equation is considered that describes the field created by a contour with two axes of symmetry. The purpose of the study is to find a fundamental solution to this equation, which can later be used when solving boundary value problems.

The wandering subspace property and Shimorin’s condition of shift operator on the weighted Bergman spaces

In the present paper, we first study the wandering subspace property of the shift operator on the $$I_{a}$$ I a type zero based invariant subspaces of the weighted Bergman spaces $$L_{a}^{2}(dA_{n})(n=0,2)$$ L a 2 ( d A n ) ( n = 0 , 2 ) via the spectrum of some Toeplitz operators on the Hardy space $$H^{2}$$ H 2 . Second, we give examples to show that Shimorin’s condition for the shift operator fails on the $$I_{a}$$ I a type zero based invariant subspaces of the weighted Bergman spaces $$L_{a}^{2}(dA_{\alpha })(\alpha >0)$$ L a 2 ( d A α ) ( α > 0 ) .

The Spectrum of Mapping Ideals of Type Variable Exponent Function Space of Complex Variables with Some Applications

The topological and geometric behaviors of the variable exponent formal power series space, as well as the prequasi-ideal construction by s -numbers and this function space of complex variables, are investigated in this article. Upper bounds for s -numbers of infinite series of the weighted n th power forward and backward shift operator on this function space are being investigated, with applications to some entire functions.

A GENERALIZATION OF THE SHIFT OPERATOR

Several approaches are known to generalize the shift operator in the complex domain. Specific generalization procedures lead to significantly different operators of the shift type even in one specific area of complex analysis. In this paper, a certain general operator of the shift type is defined. The properties of this operator are studied and the question of the continuity of this definition is considered. The properties of a certain operator to a certain extent re-peat the properties of the previously studied operators of the shift type. This allows us to speak of the possibility of extending the main results on spectral synthesis in the complex domain to convolutional equations of a more general form.

Entire functions of restricted hyper-order sharing a set of two small functions IM with their linear c-shift operators

PurposeThe paper aims to build the relationship between an entire function of restricted hyper-order with its linear c-shift operator.Design/methodology/approachStandard methodology for papers in difference and shift operators and value distribution theory have been used.FindingsThe relation between an entire function of restricted hyper-order with its linear c-shift operator was found under the periphery of sharing a set of two small functions IM (ignoring multiplicities) when exponent of convergence of zeros is strictly less than its order. This research work is an improvement and extension of two previous papers.Originality/valueThis is an original research work.

Do equidistant energy levels necessitate a harmonic potential?

Experimental results from literature show equidistant energy levels in thin Bi films on surfaces, suggesting a harmonic oscillator description. Yet this conclusion is by no means imperative, especially considering that any measurement only yields energy levels in a finite range and with a nonzero uncertainty. Within this study we review isospectral potentials from the literature and investigate the applicability of the harmonic oscillator hypothesis to recent measurements. First, we describe experimental results from literature by a harmonic oscillator model, obtaining a realistic size and depth of the resulting quantum well. Second, we use the shift-operator approach to calculate anharmonic non-polynomial potentials producing (partly) equidistant spectra. We discuss different potential types and interpret the possible modeling applications. Finally, by applying nth order perturbation theory we show that exactly equidistant eigenenergies cannot be achieved by polynomial potentials, except by the harmonic oscillator potential. In summary, we aim to give an overview over which conclusions may be drawn from the experimental determination of energy levels and which may not.