Difference Methods for Boundary Value Problems in Ordinary Differential Equations

A general theory of difference methods for problems of the form Ny ≡ y' - f(t,y) = O, a ≦ t ≦ b, g(y(a),y(b))= 0, is developed. On nonuniform nets, t_0 = a, t_j = t_(j-1) + h_j, 1 ≦ j ≦ J, t_J = b, schemes of the form N_(h)u_j = G_j(u_0,•••,u_J) = 0, 1 ≦ j ≦ J, g(u_0,u_J) = 0 are considered. For linear problems with unique solutions, it is shown that the difference scheme is stable and consistent for the boundary value problem if and only if, upon replacing the boundary conditions by an initial condition, the resulting scheme is stable and consistent for the initial value problem. For isolated solutions of the nonlinear problem, it is shown that the difference scheme has a unique solution converging to the exact solution if (i) the linearized difference equations are stable and consistent for the linearized initial value problem, (ii) the linearized difference operator is Lipschitz continuous, (iii) the nonlinear difference equations are consistent with the nonlinear differential equation. Newton’s method is shown to be valid, with quadratic convergence, for computing the numerical solution

Hidden in Plain Sight: Achieving More Just Results in Hostile Work Environment Sexual Harassment Cases by Re-Examining Supreme Court Precedent

Control of a hydraulic crane is considered. Due to the oscillatory character of the system smooth the operation of the crane is a demanding task. In order to improve the handling properties feedback control of the crane is studied. Based on linearized models feedback regulators of both LQG and PID type are designed. The feedback is based on position, pressure and acceleration measurements. Since the properties of the system change with load and operating point adaptive control is also introduced. The use of accelerometer signals for impact detection is also discussed. The proposed solutions are tested in both simulations and experiments on a real crane

Response functions of cold neutron matter: density fluctuations

We compute the finite temperature density response function of nonrelativistic cold fermions with an isotropic condensate. The pair-breaking contribution to the response function is evaluated in the limit of small three-momentum transfers q within an effective theory which exploits series expansion in powers of small q/p_F, where p_F is the Fermi momentum. The leading order O(q^2) contribution is universal and depends only on two fundamental scales, the Fermi energy and the pairing gap. The particle-hole Landau Fermi-liquid interaction contributes first at the next-to-leading-order O(q^4). The scattering contribution to the polarization tensor is nonperturbative (in the above sense) and is evaluated numerically. The spectral functions of density fluctuations are constructed and the relevance of the q^2 scaling for the pair-breaking neutrino emission from neutron stars is discussed.Comment: v2: 11 pages, 4 figures, matches published version

Liquid rocket metal tanks and tank components

Significant guidelines are presented for the successful design of aerospace tanks and tank components, such as expulsion devices, standpipes, and baffles. The state of the art is reviewed, and the design criteria are presented along with recommended practices. Design monographs are listed

Quantum Cluster Variables via Serre Polynomials

For skew-symmetric acyclic quantum cluster algebras, we express the quantum $F$-polynomials and the quantum cluster monomials in terms of Serre polynomials of quiver Grassmannians of rigid modules. As byproducts, we obtain the existence of counting polynomials for these varieties and the positivity conjecture with respect to acyclic seeds. These results complete previous work by Caldero and Reineke and confirm a recent conjecture by Rupel.Comment: minor corrections, reference added, example 4.3 added, 38 page

A-infinity algebra of an elliptic curve and Eisenstein series

We compute explicitly the A-infinity structure on the Ext-algebra of the collection $({\mathcal O}_C, L)$, where $L$ is a line bundle of degree 1 on an elliptic curve $C$. The answer involves higher derivatives of Eisenstein series.Comment: 13 pages, 3 figures; v3: added remark on the limit at the cus

His story/her story: A dialogue about including men and masculinities in the women’s studies curriculum

The article discusses the issue of inclusion of men and masculinities in the Women\u27s Studies curriculum. Women\u27s Studies programs were started to compensate for the male domination in the academics. Women\u27s Studies presented a platform where scholarship for women was produced and taken seriously, female students and faculty could find their say or voice, and theoretical investigations required for the advancement of the aims of the women\u27s movement could take place. If the academy as a whole does not sufficiently integrate Women\u27s Studies into the curriculum, integrating Men\u27s Studies into Women\u27s Studies might end up further marginalizing Women\u27s Studies by decreasing the number of classroom hours students spend engaging women\u27s lives and feminist scholarship. Such an integration would presents an another form of male privilege, with men manipulating their way into the only branch of scholarship that has consistently focused on women. On a ground level, feminist scholars are apprehensive that a move from a Women\u27s Studies program to a Gender Studies program will reduce the political aspect of women\u27s programs