Dimensional Modules Research Articles

Explicit construction of irreducible modules for $$U_q(\mathfrak {gl}_n)$$ U q ( gl n )

We construct new families of $$U_q(\mathfrak {gl}_n)$$ -modules by continuation from finite dimensional representations. Each such module is associated with a combinatorial object—admissible set of relations. More precisely, we prove that any admissible set of relations leads to a family of irreducible $$U_q(\mathfrak {gl}_n)$$ -modules. Finite dimensional and generic modules are particular cases of this construction.

On Fusion Procedure For The Two-Parameter Quantum Algebra In Type A

Finite dimensional irreducible modules of the two-parameter quantum enveloping algebra $U_{r,s}(\mathfrak{sl}_n)$ are explicitly constructed using the fusion procedure when $rs^{-1}$ is generic. This provides an alternative and combinatorial description of the Schur-Weyl duality for the two-parameter quantum linear algebras of type $A$.

Hybrid model with dynamical sources for heavy-ion collisions at BES energies

We develop a (3+1)-dimensional hybrid evolution model for heavy-ion collisions with dynamical sources for the energy-momentum tensor and baryon current. During an initial pre-equilibrium stage based on UrQMD, the four-momenta and baryon numbers carried by secondary particles created within UrQMD are fed continuously, after a short thermalization time, into a (3+1)-dimensional viscous hydrodynamic evolution module including baryon transport. The sensitivity of the initial conditions to model parameters and the effect of baryon diffusion on the hydrodynamic evolution are studied.

Jet modules for the centerless Virasoro-like algebra

In this paper, we studied the jet modules for the centerless Virasoro-like algebra which is the Lie algebra of the Lie group of the area-preserving diffeomorphisms of a [Formula: see text]-torus. The jet modules are certain natural modules over the Lie algebra of semi-direct product of the centerless Virasoro-like algebra and the Laurent polynomial algebra in two variables. We reduce the irreducible jet modules to the finite-dimensional irreducible modules over some infinite-dimensional Lie algebra and then characterize the irreducible jet modules with irreducible finite dimensional modules over [Formula: see text]. To determine the indecomposable jet modules, we use the technique of polynomial modules in the sense of [Irreducible representations for toroidal Lie algebras, J. Algebras 221 (1999) 188–231; Weight modules over exp-polynomial Lie algebras, J. Pure Appl. Algebra 191 (2004) 23–42]. Consequently, indecomposable jet modules are described using modules over the algebra [Formula: see text], which is the “positive part” of a Block type algebra studied first by [Some infinite-dimensional simple Lie algebras in characteristic [Formula: see text] related to those of Block, J. Pure Appl. Algebra 127(2) (1998) 153–165] and recently by [A [Formula: see text]-graded generalization of the Witt-algebra, preprint; Classification of simple Lie algebras on a lattice, Proc. London Math. Soc. 106(3) (2013) 508–564]).

Quasi-one-dimensional nanoscale modulation as sign of nematicity in iron pnictides and chalcogenides

Impurity scattering is found to lead to quasi-one dimensional nanoscale modulation of the local density of states in the iron pnictides and chalcogenides. This `quasiparticle interference' feature is remarkably similar across a wide variety of pnictide and chalcogenide phases, suggesting a common origin. We show that a unified understanding of the experiments can be obtained by simply invoking a four-fold symmetry breaking $d_{xz}-d_{yz}$ orbital splitting, of a magnitude already suggested by the experiments. This can explain the one-dimensional characteristics in the local density of states observed in the orthorhombic nematic, tetragonal paramagnetic, as well as the spin-density wave and superconducting states in these materials.

Surface/Interfacial Engineering of Inorganic Low-Dimensional Electrode Materials for Electrocatalysis.

Exploitation of highly active and cost-effective electrode materials for the design of new types of renewable energy storage and conversion systems has been tremendously stimulated by the higher attention being paid to global energy security and invention of alternative clean sustainable energy technologies. Low-dimensional solid materials with special atomic and electronic structures are deemed desirable platforms for establishing clear relationships between surface/interface structure characteristics and electrocatalytic activity, representing enormous potential in the pursuit of high-performance electrocatalysts. Recent achievements revealed that surface and interfacial atomic engineering is capable of achieving novel physical and chemical properties as well as superior synergistic effects in inorganic low-dimensional nanomaterials for electrocatalysis. Compared to bulk counterparts, the electronic structure in the surface of inorganic low-dimensional nanomaterials is more sensitive to and can thus be regulated more easily by surface and interfacial modification strategies, resulting in greatly optimized electrocatalytic performance. In this Account, we focus on recent progress in surface and interfacial modification strategies to efficaciously engineer the electrocatalytic performance of inorganic low-dimensional electrode materials. We summarize several important regulation strategies of dimensional confinement, incorporation, surface reconstruction, interface modulation, and defect engineering, which immensely optimize the spin configuration, electrical conductivity, catalytic active site exposure, and reaction energy barrier of inorganic electrode material. At dimensionally confined atomic-scale thickness, more surface-facet atoms are exposed as active sites, which provide an ideal platform for applying surface incorporation and defect engineering, subsequently producing more catalytic active sites and better adsorption free energy for the improvement of catalytic activity. Moreover, regulation of the interfacial character of electrode materials, such as the surface strain, contact area, and bridged bonds, can optimize the electron transfer capacity and reaction kinetics process. On the other hand, once exposed to a strong alkaline solution under oxidizing potentials, the real active layer of electrode materials (such as transition-metal sulfides, nitrides, and phosphides) could be activated by a surface reconstruction strategy, realizing a unique core-shell structure with a highly conductive electron transfer channel inside and highly active catalytic sites outside for electrocatalysis. Based on these points of view, focusing on inorganic low-dimensional electrode materials, the proper choice of surface and interfacial modification strategies would effectively modulate their electrocatalytic activity, realizing unlimited potential applications in promising areas of electrocatalytic water splitting, rechargeable metal batteries, and fuel cells. Overall, we anticipate that surface and interfacial regulation approaches can provide a new understanding of the design of inorganic electrode materials, facilitating the rapid promotion of electrocatalytic performance in electrode materials for electrocatalysis.

Magnetic Hofstadter butterfly and its topologically quantized Hall conductance

The energy spectrum of massless Dirac fermions in graphene under two dimensional periodic magnetic modulation having square lattice symmetry is calculated. We show that the translation symmetry of the problem is similar to that of the Hofstadter or TKNN problem and in the weak field limit the tight binding energy eigenvalue equation is indeed given by Harper Hofstadter hamiltonian. We show that due to its magnetic translational symmetry the Hall conductivity can be identified as a topological invariant and hence quantized. We thus extend the idea of Quantum Hall Effect to magnetically modulated two dimensional electron system. Finally we indicate possible experimental systems where this may be verified.

Lower Ionospheric Plasma‐Chemical Evolution and VLF Signal Modulation by a Series of SGR X‐Ray Bursts: Numerical Simulation With an Ion‐Chemistry Model

AbstractThe X‐ray and gamma ray radiation from astrophysical transient sources, like X‐ray bursts from soft gamma repeaters (SGRs) and gamma ray bursts (GRBs), can affect the plasma properties of the lower ionosphere and middle atmosphere. Multiple very low frequency (VLF) receivers in South America, with an unprecedented high time resolution of 20 ms, detected one such series of bursts from SGR J1550‐5418 on 22 January 2009. Due to lack of other suitable means of observation corresponding to the lower part of Earth's ionosphere (∼60–100 km), the VLF detection and analysis of transient ionizing events (mostly of solar origin) has emerged as an excellent method to investigate various chemical and plasma characteristics at these heights. Extragalactic events, like SGR bursts and GRBs, with sharp modulation in their radiation time profile and very high energy photon abundances provide most unique opportunities of such studies with the possibility of extending even lower heights in the atmosphere. Here, for the first time, an extensive computer model, consisting of the combination of Monte Carlo ionization rate computation, a one dimensional atmospheric chemistry module, and VLF waveguide mode calculation, for the reconstruction of VLF signal modulation produced by SGR X‐ray burst starting from the observed spectrum and lightcurve of the event is presented. We gain some valuable insight on the nature of chemical and dynamic evolution over the entire height range of the atmosphere examined from the exercise.

KNOCK DOWN BAMBOO WALL PANEL

Abstract- Indonesia often experiences natural disasters, therefore a transitional residential building is needed for victims who are able to build quickly and easily in mobilization. Bamboo is a local material that exists in Indonesia and has a high sustainability to be used as building materials. The appropriate principle between the characteristics of bamboo and the needs of transitional buildings where used as wall materials. The knock down bamboo wall panel is the answer of the need for fast and easy work in mobilization.The research method used is qualitative descriptive of two study object and design experiment of prototype 1: 1. Researchers will conduct a study of bamboo walls on two study objects Blooming Bamboo Home dan Soe Ker Tie House, also meetings of any deficiencies and advantages from aspects of form, function and context, and construction. Forms include material used, basic dimensional modules, wall weight, and the ability to re-modify walls. Functions and Contexts include the space privacy, resistance, and behavior of walls against wind, solar heat, lighting, and rain. Construction covers the way of bamboo processing into wall panels, connection systems, and can be done massively by the crowd. Potential bamboo wall variants to be explored will be evaluated and developed for the better and new alternative of other wall panels also considered.The most efficient bamboo knock down panels are bamboo slats and woven bamboo booths as massive walls, woven bamboo and bamboo modified blades I as semi-open walls, modified bamboo blades II and polikarbonate as open walls. The most appropriate connection system used in knock down bamboo wall panels is the gypsum screw connection for bamboo wall panel frame joints, bolt nuts and iron plates for knock down bamboo wall panel connections with structures and connections between wall panels. Keywords: Knock down, Bamboo, Sustainable, Wall panel

Reduced-Dimensional α-CsPbX3 Perovskites for Efficient and Stable Photovoltaics

Summary Inorganic CsPbX3 perovskites have gained great attention owing to their excellent thermal stability and carrier transport properties. However, the power conversion efficiency (PCE) of solution-processed CsPbX3 perovskite solar cells is still far inferior to that of their hybrid analogues. Insufficient film thickness and undesirable phase transition are the two major obstacles limiting their device performance. Here, we show that by adopting a new precursor pair, cesium acetate (CsAc) and hydrogen lead trihalide (HPbX3), we were able to overcome the notorious solubility limitation for Cs precursors to fabricate high-quality CsPbX3 perovskite films with large film thickness (∼500 nm). We further introduced a judicious amount of phenylethylammonium iodide (PEAI) into the system to induce reduced-dimensional perovskite formation. Unprecedentedly, the resulting quasi-2D perovskites significantly suppressed undesirable phase transition and thus reduced the film's trap density. Following this approach, we reported a state-of-the-art PCE to date, 12.4%, for reduced-dimensional α-CsPbI3 perovskite photovoltaics with greatly improved performance longevity.

Structural modulation and band gap optimisation of electrochemically anodised TiO2 nanotubes

This analytical study highlights the effects of dimensional modulations on the characteristic properties of anodically grown Titania nanotubes. Titania nanotubes were grown using electrochemical anodization method employing a two-electrode system. The as-grown nanotubes with different dimensions were characterized in order to study their structural, electrical and optical properties. The investigation reveals that the impact of dimension was pivotal in tuning the band gap of these anodically grown Titania nanotubes which asserts its successful application in various fields. The desired dimensional modulation of the nanotubes was achieved by changing the corresponding anodising voltage. This study also employs a remedial two step anodization technique in addition to the conventional one step method and presents its distinctive edge over the other as established by various characterisation techniques. The comparative variations in the structural and crystallite dimensions of the Titania nanotubes anodised by two different methods were investigated by Field Emission Scanning Electron Microscopy and X-Ray Diffraction spectroscopy respectively, while the band gap tuning ability as well as absorption characteristics were determined by UV-Diffuse Reflectance spectroscopy. Finally, the effective changes in the band gap were corroborated by analysing the field effect dark and photo-conductive nature of the two materials.

The periplectic Brauer algebra

We study the periplectic Brauer algebra introduced by Moon in the study of invariant theory for periplectic Lie superalgebras. We determine when the algebra is quasi-hereditary, when it admits a quasi-hereditary 1-cover and, for fields of characteristic zero, describes the block decomposition. To achieve this, we also develop theories of Jucys–Murphy elements, Bratteli diagrams, Murphy bases, obtain a Humphreys-BGG reciprocity relation and determine some decomposition multiplicities of cell modules. As an application, we determine the blocks in the category of finite dimensional integrable modules of the periplectic Lie superalgebra.

Glucose Sensing with Phenylboronic Acid Functionalized Hydrogel-Based Optical Diffusers.

Phenylboronic acids have emerged as synthetic receptors that can reversibly bind to cis-diols of glucose molecules. The incorporation of phenylboronic acids in hydrogels offers exclusive attributes; for example, the binding process with glucose induces Donnan osmotic pressure resulting in volumetric changes in the matrix. However, their practical applications are hindered because of complex readout approaches and their time-consuming fabrication processes. Here, we demonstrate a microimprinting method to fabricate densely packed concavities in phenylboronic acid functionalized hydrogel films. A microengineered optical diffuser structure was imprinted on a phenylboronic acid based cis-diol recognizing motif prepositioned in a hydrogel film. The diffuser structure engineered on the hydrogel was based on laser-inscribed arrays of imperfect microlenses that focused the incoming light at different focal lengths and direction resulting in a diffused profile of light in transmission and reflection readout modes. The signature of the dimensional modulation was detected in terms of changing focal lengths of the microlenses due to the volumetric expansion of the hydrogel that altered the diffusion spectra and transmitted beam profile. The transmitted optical light spread and intensity through the sensor was measured to determine variation in glucose concentrations at physiological conditions. The sensor was integrated in a contact lens and placed over an artificial eye. Artificial stimulation of variation in glucose concentration allowed quantitative measurements using a smartphone’s photodiode. A smartphone app was utilized to convert the received light intensity to quantitative glucose concentration values. The developed sensing platform offers low cost, rapid fabrication, and easy detection scheme as compared to other optical sensing counterparts. The presented detection scheme may have applications in wearable real-time biomarker monitoring devices at point-of-care settings.

Generators versus projective generators in abelian categories

Let A be an abelian category. We prove that if A admits a generator M with EndA(M) right artinian, then A admits a projective generator. If A is further assumed to be Grothendieck, then this implies that A is equivalent to a module category. When A is Hom-finite over a field k, the existence of a generator is the same as the existence of a projective generator, and in case there is such a generator, A has to be equivalent to the category of finite dimensional right modules over a finite dimensional k-algebra. We also show that when A is a length category, then there is a one-to-one correspondence between exact abelian extension-closed subcategories of A and collections of Hom-orthogonal Schur objects in A.

Common Mode Voltage Reduction Using 3D-SVPWM for 3-level CI-NPC Inverter with Hybrid Energy System

This paper elucidates Common Mode Voltage (CMV) reduction in transformerless 3-phase 3-level Coupled Inductor Neutral Point (CI-NPC) Clamped Inverter with Hybrid Energy System. The three dimensional Space Vector Pulse Width Modulation (3D-SVPWM) with Nearest State Vector (NSV) is implemented to reduce the CMV by proper selection of medium, large and small vectors in 3D cubic space region. This NSV scheme in addition to CMV reduction, reduces the capacitor voltage balancing issues and minimizes switching losses. The proposed control provides full utilization of dc link voltage with reduced harmonics. This 3-level CI-NPC inverter is energized by hybrid energy source which includes photovoltaic system and wind energy system. The results obtained for the proposed scheme through simulation and experimental setup is compared with the conventional 2D-SVPWM and 3D-SVPWM scheme. From the compared results it is evident that the proposed scheme reduces CMV to a larger extent than 2D and 3D-SVPWM control. The simulation and experimental results are verified using matlab-simulink and FPGA-Spartan-6 controller respectively.

Dual Polar Graphs, a nil-DAHA of Rank One, and Non-Symmetric Dual q-Krawtchouk Polynomials

Let $\Gamma$ be a dual polar graph with diameter $D \geqslant 3$, having as vertices the maximal isotropic subspaces of a finite-dimensional vector space over the finite field $\mathbb{F}_q$ equipped with a non-degenerate form (alternating, quadratic, or Hermitian) with Witt index $D$. From a pair of a vertex $x$ of $\Gamma$ and a maximal clique $C$ containing $x$, we construct a $2D$-dimensional irreducible module for a nil-DAHA of type $(C^{\vee}_1, C_1)$, and establish its connection to the generalized Terwilliger algebra with respect to $x$, $C$. Using this module, we then define the non-symmetric dual $q$-Krawtchouk polynomials and derive their recurrence and orthogonality relations from the combinatorial points of view. We note that our results do not depend essentially on the particular choice of the pair $x$, $C$, and that all the formulas are described in terms of $q$, $D$, and one other scalar which we assign to $\Gamma$ based on the type of the form.

Indecomposable generalized weight modules over the algebra of polynomial integro-differential operators

For the algebra L= K of polynomial integro-differential operators over a field K of characteristic zero, a classification of indecomposable, generalized weight L-modules of finite length is given. Each such module is an infinite dimensional uniserial module. Ext-groups are found between indecomposable generalized weight modules, it is proven that they are finite dimensional vector spaces.

Finite dimensional simple modules of deformed current Lie algebras

The deformed current Lie algebra was introduced in [4] to study the representation theory of cyclotomic q-Schur algebras at q=1. In this paper, we classify finite dimensional simple modules of deformed current Lie algebras.

A combinatorial approach to the exponents of Moore spaces

In this article, we give a combinatorial approach to the exponents of Moore spaces. Our result states that the projection of the $$p^{r+1}$$ -power map of the loop space of the $$(2n+1)$$ -dimensional mod $$p^r$$ Moore space to its atomic piece containing the bottom cell $$T^{2n+1}\{p^r\}$$ is null homotopic for $$n>1$$ , $$p>3$$ and $$r>1$$ . This result strengthens the classical result that $$\Omega T^{2n+1}\{p^r\}$$ has an exponent $$p^{r+1}$$ .

A bispectral q-hypergeometric basis for a class of quantum integrable models

For the class of quantum integrable models generated from the q−Onsager algebra, a basis of bispectral multivariable q−orthogonal polynomials is exhibited. In the first part, it is shown that the multivariable Askey-Wilson polynomials with N variables and N + 3 parameters introduced by Gasper and Rahman [Dev. Math. 13, 209 (2005)] generate a family of infinite dimensional modules for the q−Onsager algebra, whose fundamental generators are realized in terms of the multivariable q−difference and difference operators proposed by Iliev [Trans. Am. Math. Soc. 363, 1577 (2011)]. Raising and lowering operators extending those of Sahi [SIGMA 3, 002 (2007)] are also constructed. In the second part, finite dimensional modules are constructed and studied for a certain class of parameters and if the N variables belong to a discrete support. In this case, the bispectral property finds a natural interpretation within the framework of tridiagonal pairs. In the third part, eigenfunctions of the q−Dolan-Grady hierarchy are considered in the polynomial basis. In particular, invariant subspaces are identified for certain conditions generalizing Nepomechie’s relations. In the fourth part, the analysis is extended to the special case q = 1. This framework provides a q−hypergeometric formulation of quantum integrable models such as the open XXZ spin chain with generic integrable boundary conditions (q ≠ 1).