Analytical Solution of the Dynamics Equations for a Wave Solid-State Gyroscope Using the Angular Rate Linear Approximation

The exact solution is provided of the dynamics equation for an elastic inextensible ring being the basic model of a wave solid-state gyroscope with the linear law of the base angular rotation rate alteration. This solution is presented in terms of the parabolic cylinder functions (Weber function). Asymptotic approximations are used in the device certain operating modes. On the basis of the solution obtained, the analytical solution to the equation of the ring dynamics in case of piecewise linear approximation of the angular rate arbitrary profile on a time grid is derived. This significantly expands the class of angular rate dependences, for which the solution could be written down analytically. Earlier, in addition to the simplest case of constant angular rate, solutions were obtained for angular rate varying according to the square root law with time (Airy function), as well as according to the harmonic law (Mathieu function). Error dependence of such approximation on the discretization step in time is estimated numerically. Results obtained make it possible to reduce the number of operations, when it is necessary to study long-term evolutions of the dynamic system oscillations, as well as to quantitatively and qualitatively control convergence of finite-difference schemes in solving dynamics equations for a wave solid-state gyroscope with the ring resonator

Traverse electric field effect on wave vector filtering in a magnetically modulated semiconductor nanostructure

We theoretically study the effect of traverse electric field on wave vector filtering (WVF) in a magnetically modulated nanostructure, which can be constructed by patterning ferromagnetic (FM) stripes on top and bottom of GaAs/Al[Formula: see text]Ga[Formula: see text]As heterostructure. Using the transfer matrix method, electric field-dependent transmission is calculated by using Weber function for electrons across the structure. We find that WVF efficiency is manipulable by adjusting direction or strength of electric field. Thus, an electrically-tunable momentum filtering device can be obtained.

On a problem of Hasse and Ramachandra

Let K be an imaginary quadratic field, and let 𝔣 be a nontrivial integral ideal of K. Hasse and Ramachandra asked whether the ray class field of K modulo 𝔣 can be generated by a single value of the Weber function. We completely resolve this question when 𝔣 = (N) for any positive integer N excluding 2, 3, 4 and 6.

Summations of Schlömilch series containing anger function terms

The main aim of this article is to establish certain closed expressions for the Schlömilch series which members contain Anger function 𝐉νin order to generalize already known results. Closed expressions for the Schlömilch series with members containing some Lommel functions of the first kindsμ,νand also a Weber function 𝐄νand Struve function 𝐇νare derived as a by–product of these results.

A Location Allocation Model for a Territorial Design Problem with Dense Demand

The authors present in this work a proposal that allows establishing the relationships between the facilities location problem and the client allocation within a dense demand environment in territorial design. This proposal can be seen as a basic methodology to give support to the decision making. The use of this application lets one know the production facilities location, warehouses or distribution centers in a geographical space division. On the other hand, solving the client's dense demand for goods or services, means finding the location of facilities in a populated geographic territory, where the population has a demand for services in a constant basis. Finding the location is obtaining the decimal geographical coordinates in longitude, latitude where the facility is located, such that the product or service transport costs the least. The implications and practical benefits of the results from this work allow an organization to be able to design an efficient logistics plan in benefit of its supply chain. The problem the authors present is a territorial design and optimization one due to the fact that the required territorial partition demands the creation of compact zones where the minimum distance between the geographical objects is implicitly optimized. This problem belongs to the NP-hard class, where the use of a metaheuristic to attain approximated solutions becomes a necessity, Variable Neighborhood Search was chosen because it achieves good solutions for this kind of problems. Once the territory has been partitioned into k zones where the centroid of each zone is the distribution center, as a first step the authors proceed to apply the dense demand with continuous functions and this is the main original contribution of this paper: Finding the location of facilities inside a territory where the population has a dense demand for services. The location obtained means having available the decimal geographic coordinates in longitude and latitude from the location point in such a way that the products or services transfer has a minimum cost. Finally the Weber function is minimized, which weights are a function that represents the population's demand in every territory, multiplied by the Euclidean distance between the potential location points and demand points.