Narrow Results

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.

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.

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.

A prerequisite for a synthetic description of the learning and memory (LM), neural bases is a model of the brain. The model we have adopted is based on functional anatomy and consists of three interacting systems. The first, R for representation, is made of the neurons which code sensory information or motor programs with the highest precision. The second, A for activation, comprises the neurons which are most directly involved in arousal and motivation. The third system, S for supervision, controls goal-directed behaviors. The best illustration of its functions is the “voluntary act” in humans: it involves a representation of a goal and of the appropriate strategies, the evaluation of the results and the correction of errors.

The memory system is not an anatomically separate entity but a set of interactions between R, A and S. In these interactions, the three systems have different though complementary functions. R is mainly involved in encoding and storage. S plays a role in encoding and retrieval through the control of attention and cognitive strategies. Structures of A, which modulate R and S activities, are involved in all stages of memory processes. Different types of LM set into play different types of interactions between R, A and S.

Within this general scheme, we considered data from different levels of organization, from the whole brain to the molecule, through intermediates such as small networks (for example, the cortical column). Finally, an attempt is made at defining the perspectives for future research. Among its main objectives are the integration of LM bases in the neurobiology of the whole behavior, the genetic and developmental factors, new therapies for improving memory in aged and demented people, the design of formalisms able to represent large-scale neural networks.

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.

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.

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.