Narrow Results

This publication considers the use of a variety of additive manufacturing techniques in the development of wireless modules and sensors. The opportunities and advantages of these manufacturing techniques are explored from an application point of view. We discuss first the origami (4D-printed) structures which take advantage of the ability to alter the shape of the inkjet-printed conductive traces on the paper substrate to produce a reconfigurable behavior. Next, focus is shifted towards the use of additive manufacturing technology to develop skin-like flexible electrical system for wireless sensing applications. We then discuss the development of a fully flexible energy autonomous body area network for autonomous sensing applications, the system is fabricated using 3D and inkjet printing techniques. Finally, an integration of inkjet and 3D printing for the realization of efficient mm-wave 3D interconnects up to 60GHz is discussed.

This publication provides an overview of additive manufacturing techniques including Inkjet, 3D and 4D printing methods. The strengths, opportunities and advantages of this array of manufacturing techniques are evaluated at different scales. We discuss first the applicability of additive manufacturing techniques at the device scale including the development of origami inspired tunable RF structures as well as the development of skin-like conformal, flexible systems for wireless/IoT, Smartag and smart city applications. We then discuss application at the package scale with on package printed antennas and functional packaging applications. Following this, there is a discussion of additive manufacturing techniques in applications at the die scale such as 3D printed interconnects. The paper is concluded with an outlook on future advancements at the component scale with the potential for fully printed passive components.

Applying network science to investigate the complex systems has become a hot topic. In neuroscience, understanding the architectures of complex brain networks was a vital issue. An enormous amount of evidence had supported the brain was cost/efficiency trade-off with small-worldness, hubness and modular organization through the functional MRI and structural MRI investigations. However, the T1-weighted/T2-weighted (T1w/T2w) ratio brain networks were mostly unexplored. Here, we utilized a KL divergence-based method to construct large-scale individual T1w/T2w ratio brain networks and investigated the underlying topological attributes of these networks. Our results supported that the T1w/T2w ratio brain networks were comprised of small-worldness, an exponentially truncated power–law degree distribution, frontal-parietal hubs and modular organization. Besides, there were significant positive correlations between the network metrics and fluid intelligence. Thus, the T1w/T2w ratio brain networks open a new avenue to understand the human brain and are a necessary supplement for future MRI studies.

A modularity concept for structuring and developing large logic programs and logical knowledge bases is presented. The concept is motivated from work in the field of algebraic specification, and enforces an extreme modularity discipline that goes beyond the one found in imperative or logic programming languages. As concrete programming languages (respectively knowledge representation formalisms), we consider Horn logic and equational logic programming. We give formal semantics for single modules and discuss correctness and verification issues. Large systems are constructed as interconnections of single modules. We introduce the so-called module operations of composition, actualization, and union, and give results concerning compositionality of semantics and correctness preservation.

We provide conditions guaranteeing that a given element of a simple algebraic group G has a fixed vector in every nonzero G-module, and deduce similar results for finite Chevalley groups.

This is an introduction to Bret Tilson's paper "Modules".

This paper introduces the notion of a module over a graph and defines the wreath product and derived module of a relational morphism in this context.

In this paper we study the ℤ-module A₂ of two-chord diagrams for knots with zero winding number in the solid torus KST₀, which is needed in studying the type-two invariants for knots in KST₀. We show that this module (or abelian group), which is given as a presentation with infinite number of generators and an infinite number of relations, is a free infinitely generated module. Moreover, we show that this module is isomorphic to the direct sum of three free modules that are easier to understand.

We introduce a natural filtration in the space of knots and singular knots in the solid torus, and start the study of the type-two Vassiliev invariants with respect to this filtration. The main result of the work states that any such invariant within the second term of this filtration in the space of knots with zero winding number is a linear combination of seven explicitly described Gauss diagram invariants. This introduces a basis (and a universal invariant) for the type-two Vassiliev invariants for knots with zero winding number. Then we formalize the problem of exploring the set of all type-two invariants for knots with zero winding number.

In applying the boundary element method to an acoustic interior problem modeled as a single domain, even a small change of the cavity geometry affects the whole system matrix. Thus, calculating sensitivities for each intermediate shape is performed independently during iterations for an optimum shape. By utilizing the sub-domain modularization capability of the MBEM, however, the matrix inversion task is performed only once for the initial shape during whole iterations. This can reduce the total computational costs of finding an optimum shape design and the computational efficiency increases as the number of iterations increases. A demonstration example is given by a two-dimensional automotive interior cavity.

We characterize rings over which every cotorsion module is pure injective (Xu rings) in terms of certain descending chain conditions and the Ziegler spectrum, which renders the classes of von Neumann regular rings and of pure semisimple rings as two possible extremes. As preparation, descriptions of pure projective and Mittag–Leffler preenvelopes with respect to so-called definable subcategories and of pure generation for such are derived, which may be of interest on their own. Infinitary axiomatizations lead to coherence results previously known for the special case of flat modules. Along with pseudoflat modules we introduce quasiflat modules, which arise naturally in the model-theoretic and the category-theoretic contexts.

Let V be a simple vertex operator algebra satisfying the following conditions: (i) V_(n) = 0 for n < 0, V₍₀₎ = ℂ1 and V′ is isomorphic to V as a V-module. (ii) Every ℕ-gradable weak V-module is completely reducible. (iii) V is C₂-cofinite. (In the presence of Condition (i), Conditions (ii) and (iii) are equivalent to a single condition, namely, that every weak V-module is completely reducible.) Using the results obtained by the author in the formulation and proof of the general version of the Verlinde conjecture and in the proof of the Verlinde formula, we prove that the braided tensor category structure on the category of V-modules is rigid, balanced and nondegenerate. In particular, the category of V-modules has a natural structure of modular tensor category. We also prove that the tensor-categorical dimension of an irreducible V-module is the reciprocal of a suitable matrix element of the fusing isomorphism under a suitable basis.

The restrictions of irreducible modules over classical groups in characteristic 2 to subsystem subgroups of type A₁ × A₁ are studied. The composition factors (without their multiplicities) for restrictions of irreducible modules over A_r(K) and D_r(K) with 2-restricted highest weights are found.

A module M is called a dimension module if the Goldie (uniform) dimension satisfies the formula u(A + B) + u(A ∩ B) = u(A) + u(B) for arbitrary submodules A, B of M. Dimension modules and related notions were studied by several authors. In this paper, we study them in a more general context of modular lattices with 0 to which the notion of dimension modules can be extended in an obvious way. Some constructions available in the lattice theory framework make it possible to identify several new aspects concerning the nature of dimension lattices and modules as well as to describe a number of related properties. In particular we find a lattice which can be used to test whether a given lattice or a module satisfies the studied properties. Most of the results are obtained for lattices and then they are applied to modules. However the examples are given, when possible, in the more restrictive case of modules.

In this paper we classify non-commutative quadrics and study their homological properties. In fact we find all non-commutative algebras of degree 2 up to isomorphism and we study these algebras via their homomorphic images onto the polynomial algebra k[x,y] as well as the Ext¹(k(p), k(q))-groups, where k(p) and k(q) are one-dimensional simple modules. Moreover some general results on simple finite-dimensional modules are obtained. Some of these results are applied to the special cases of non-commutative quadrics.

We classify modules and rings with some specific properties of their intersection graphs. In particular, we describe rings with infinite intersection graphs containing maximal left ideals of finite degree. This answers a question raised in [S. Akbari, R. Nikandish and J. Nikmehr, Some results on the intersection graphs of ideals of rings, J. Algebra Appl.12 (2013) 1250200]. We also generalize this result to modules, i.e. we get the structure theorem of modules for which their intersection graphs are infinite and contain maximal submodules of finite degree. Furthermore, we omit the assumption of maximality of submodules and still get a satisfactory characterization of such modules. In addition, we show that if the intersection graph of a module is infinite but its clique number is finite, then the clique and chromatic numbers of the graph coincide. This fact was known earlier only in some particular cases. It appears that such equality holds also in the complement graph.

We give a relativization of the notions of essential, uniform, closed, injective and extending modules with respect to a left exact preradical on the ring. We also give useful examples and show that several classical properties hold for these kinds of modules.