Bias deployable grids with horizontal compound scissor-like elements: A geometric study of the folding/deployment process

Bias deployable structural units are two-way structures arranged in a rotational pattern with respect to the edges. They have interesting advantages such as robust three-dimensional operation with supports around their entire base perimeter and the exclusive use of load-bearing scissor-like elements (SLEs). However, they do not have edge trims and their resistance to angular distortion is limited. This article proposes a series of deployable bi-stable structures that address these problems and incorporate new, resilient features. A method of analysing the incompatibilities of the structural unit is developed based solely on the geometric study of the deployment process, which allows the level of incompatibility of the proposal to be graduated, varying from stress-free structures to bi-stable structures. A kinematic model of one of the proposals allows the research undertaken to be contrasted.

On a geometric study of a class of normalized functions defined by Bernoulli’s formula

The central purpose of this effort is to investigate analytic and geometric properties of a class of normalized analytic functions in the open unit disk involving Bernoulli’s formula. As a consequence, some solutions are indicated by the well-known hypergeometric function. The class of starlike functions is investigated containing the suggested class.

Algebraic Geometry of Lie Bialgebras Defined by Solutions of the Classical Yang–Baxter Equation

This paper is devoted to algebro-geometric study of infinite dimensional Lie bialgebras, which arise from solutions of the classical Yang–Baxter equation. We regard trigonometric solutions of this equation as twists of the standard Lie bialgebra cobracket on an appropriate affine Lie algebra and work out the corresponding theory of Manin triples, putting it into an algebro-geometric context. As a consequence of this approach, we prove that any trigonometric solution of the classical Yang–Baxter equation arises from an appropriate algebro-geometric datum. The developed theory is illustrated by some concrete examples.

Manin Involutions for Elliptic Pencils and Discrete Integrable Systems

We contribute to the algebraic-geometric study of discrete integrable systems generated by planar birational maps: (a) we find geometric description of Manin involutions for elliptic pencils consisting of curves of higher degree, birationally equivalent to cubic pencils (Halphen pencils of index 1), and (b) we characterize special geometry of base points ensuring that certain compositions of Manin involutions are integrable maps of low degree (quadratic Cremona maps). In particular, we identify some integrable Kahan discretizations as compositions of Manin involutions for elliptic pencils of higher degree.

TO EXISTENCE OF COMPLETELY CONTINUOUS DIFFERENTIAL REALIZATION SECOND ORDER BILINEAR SYSTEM

For a continuous nonlinear infinite-dimensional behavioristic system (dynamical system of J. Willems), a functional-geometric study of the necessary and sufficient conditions for the existence of six non-stationary coefficients-operators of the model of bilinear differential realization of this system in the class of second-order differential equations in a separable Hilbert space is carried out. The case is investigated when the simulated operators are burdened with a condition that ensures the complete continuity of the integral form of the equations of realization in the entropy setting.

A geometric study of different curves for the rotor profiles of a twin-screw compressor

This paper presents the results of comparisons among some patented solutions for profiling the contours of the rotors in twin-screw compressors. Referring to a base case where all the generating curves are circumferences, patents suggesting to replace arcs of circumference with arcs of conic sections, i.e. parabola, ellipse and hyperbola, but even a straight line segment, are presented and guidelines for rotor profile construction are reported. After setting the size of the compressor, attention is paid to the inter-lobe area, as the sum of the area between two consecutive lobes in the male rotor and of the area of the groove in the female rotor. Actually, this area is strictly related to the volume displacement. Limited to the current case study, the profile including an elliptic segment seems to be the preferable solution for higher inter-lobe area, then for higher displacement, though a number of considerations should be necessary for a broader context.