Related papers: Some open problems in the theory of composites
We begin the study of the consequences of the existence of certain infinite matrices. Our present application is to compactness of products of topological spaces.
The composite plate problem is an eigenvalue optimization problem related to the fourth order operator $(-\Delta)^2$. In this paper we continue the study started in [10], focusing on symmetry and rigidity issues in the case of the hinged…
Two questions related to elastic motions are raised and addressed. First: in which theoretical framework can the equations of motion be written for an elastic half-space put into uniform rotation? It is seen that nonlinear finite elasticity…
On base of differential biquaternions algebra and generalized functions theory the biquaternionic wave equation is considered under vector representation of its structural coefficient. Its generalized solutions are constructed, which…
Introduction to the theory of decoherence. Contents: 1. The phenomenon of decoherence: superpositions, superselection rules, decoherence by "measurements". 2. Observables as a derivable concept. 3. The measurement problem. 4. Density…
The generalized projection-tensor geometry introduced in an earlier paper is extended. A compact notation for families of projected objects is introduced and used to summarize the results of the previous paper and obtain fully projected…
Ordered pairs of proper, non-empty real projective conics can be classified modulo rigid isotopy and ambient isotopy. We characterize the classes by equations, inequations and inequalities in the coefficients of the quadratic forms defining…
We present a detailed study of the combinatorial interpretation of matrix integrals, including the examples of tessellations of arbitrary genera, and loop models on random surfaces. After reviewing their methods of solution, we apply these…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. In…
A generalized scalar-tensor theory is investigated whose cosmological term depends on both a scalar field and its time derivative. A correspondence with solutions of five-dimensional Space-Time-Matter theory is noted. Analytic solutions are…
Two dimensional electric potential maps based on voltage detection in conducting paper are common practice in many physics courses in college. Most frequently, students work on `capacitor-like' geometries with current flowing between two…
Tensor decomposition on big data has attracted significant attention recently. Among the most popular methods is a class of algorithms that leverages compression in order to reduce the size of the tensor and potentially parallelize…
One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a…
In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…
Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.
We construct an order-sharp theory for a double-porosity model in the full linear elasticity setup. Crucially, we uncover time and frequency dispersive properties of highly oscillatory elastic composites.
We offer a systematic account of decomposition of quantum systems into parts. Different decompositions (structures) are mutually linked via the proper linear canonical transformations. Different kinds of structures, as well as their…
We introduce the theoretical framework we use to study the bewildering variety of phases in condensed--matter physics. We emphasize the importance of the breaking of symmetries, and develop the idea of an order parameter through several…
Electromagnetic (EM) composites have stimulated tremendous fundamental and practical interests owing to their flexible electromagnetic properties and extensive potential engineering applications. Hence, it is necessary to systematically…
Problems related to projections on closed convex cones are frequently encountered in optimization theory and related fields. To study these problems, various unifying ideas have been introduced, including asymmetric vector-valued norms and…