The Width and Integer Optimization on Simplices With Bounded Minors of the Constraint Matrices

In this paper, we will show that the width of simplices defined by systems of linear inequalities can be computed in polynomial time if some minors of their constraint matrices are bounded. Additionally, we present some quasi-polynomial-time and polynomial-time algorithms to solve the integer linear optimization problem defined on simplices minus all their integer vertices assuming that some minors of the constraint matrices of the simplices are bounded.Comment: 12 page

The Birth of the Federation: Origins of the Russian Struggle for Democracy

Introduction Boris Yeltsin and his trusted deputies gathered around the table. A big question was supposed to be decided that day: a question that would fundamentally change the course of a nuclear superpower for decades to come. The anxiety in the room was unbearable: some deputies wiped their sweat with napkins, others silently tapped their feet underneath the table, and the rest hid their eyes in the notebooks full of information that was already well memorized by everyone inside. At last, Boris Yeltsin stood up, took several long sips from the water bottle, placed it firmly on the desk beside him and began his address to the deputies: “A republic, by which I mean a government in which the scheme of representation takes place, opens a different prospect, and promises the cure for which we are seeking. Let us examine the points in which it varies from pure democracy, and we shall comprehend both the nature of the cure and the efficacy which it must derive from the Union.

MECHANICAL RESPONSE OF LAYERED STRUCTURES WITH INTERNAL LAYERS FROM METAMATERIALS EXPOSED TO DYNAMIC LOADINGS

The article presents the results of the analysis of mechanical behavior of mechanical layered structures with metamaterial interlayers under dynamic loading. These structures can be used in lightweight structures for damping dynamic loads in transport and aerospace engineering. Structural elements with layers of the mechanical metamaterials have a low specific mass density and high specific strength characteristics. These multilayer structures have a high specific ability to absorb and dissipate the energy of external dynamic loads too. The results of numerical simulation of the response of multilayer structures to dynamic impacts obtained in this work indicate high specific energy absorption and dissipative properties, which make it possible to weaken the pulse amplitude after passing through the layered system and attenuate of cyclic impacts amplitudes. The results obtained indicate the possibility of creating effective mechanical damping structures of the type under discussion